# g50t-5849a774 · pasada 1 · log de pensamiento

## Paso 1 · nivel 1 · acción 1

**Pensamiento:**

Let me inspect the board structure.

```python
print(current_frame.shape, current_frame.level, valid_actions)
seg = current_frame.segmentation
for n in seg['nodes']:
    print(n['id'], n['color'], n['pixels'], n['boundary'][:6], n['children'])
```

```text
(64, 64) 1 ['UP', 'DOWN', 'LEFT', 'RIGHT', 'SPACE']
0 W 2649 [[0, 0], [0, 63], [62, 63], [62, 0]] [1, 2, 4, 5]
1 b 8 [[1, 1], [1, 3], [3, 3], [3, 1]] [3]
2 w 9 [[1, 5], [1, 7], [3, 7], [3, 5]] []
3 W 1 [[2, 2]] []
4 b 3 [[5, 1], [5, 3]] []
5 B 879 [[7, 13], [7, 43], [13, 43], [13, 42], [14, 41], [41
… [415 caracteres más]
```

**Pensamiento:**

Let me understand the board. There's a black region (node 5) forming the maze walls presumably. Actually node 5 is B (black) with 879 pixels, containing children: node 6 (b, blue 24 pixels, a 5x5 square at rows 8-12, cols 14-18 — with a black pixel inside at [10,16]), node 7 (R red, 82 px, a path shape), node 9 (W 25px white square at 14-18, 20-24), node 10 (W 331 px, big white region — the maze floor), node 11 (b 19 px at rows 49-55, cols 43-49 — the goal?), node 12 (b 1 px at [52,46]).
Also node 1: b 8 pixels at rows 1-3, cols 1-3 with a W pixel inside (node 3 at [2,2]) — that's a legend/key item in the top-left. Node 2: w light gray 9 px at rows 1-3 cols 5-7 — another legend item. Node 4: b 3 px at rows 5, cols 1-3 — a small blue bar (legend). Node 13: b 64 px at row 63 all columns — bottom bar (timer? or just a blue line).
Hmm, the top-left items look like a legend: blue square with black dot inside (like the player avatar?), gray square, and a small blue line.
Let me look at the ascii for the legend area and the maze to understand.
Actually the image shows: top-left there's a blue square with dark center (matching node 6 which is the blue 5x5 with black center at row 8-12... wait node 6 is 24 pixels blue with a black inside). Hmm node 1 is b 8 pixels: a 3x3 ring with white center. In the image, top-left at approximately (1,1)-(3,3) there's a blue square with black center. Hmm, the segmentation says node 1 color 'b' with 8 pixels and child node 3 color 'W' 1 pixel. So it'
… [130 caracteres más]

```python
a = current_frame.ascii.split('\n')
def crop(r0,r1,c0,c1):
    for r in range(r0,r1+1):
        print(r, a[r][c0:c1+1])
crop(0,8,0,20)
print('---')
crop(6,20,12,44)
```

```text
0 WWWWWWWWWWWWWWWWWWWWW
1 WbbbWwwwWWWWWWWWWWWWW
2 WbWbWwwwWWWWWWWWWWWWW
3 WbbbWwwwWWWWWWWWWWWWW
4 WWWWWWWWWWWWWWWWWWWWW
5 WbbbWWWWWWWWWWWWWWWWW
6 WWWWWWWWWWWWWWWWWWWWW
7 WWWWWWWWWWWWWBBBBBBBB
8 WWWWWWWWWWWWWBbbbbbBB
---
6 WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
7 WBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBW
8 WBbbbb
… [470 caracteres más]
```

**Pensamiento:**

Interesting. So the maze: black walls (B), white floor (W). The blue 5x5 block at rows 8-12, cols 14-18 is a blue square with a black pixel at center (10,16) — that looks like the "player" avatar? Actually it's a 5x5 blue with a black center dot — like the legend item at top-left (blue with dark center). Hmm, top-left legend at (1,1)-(3,3) is a blue 3x3 with a white center 'W'... wait row2: `WbWbW` → col1=b, col2=W, col3=b. So the legend item is a blue ring with white center? Hmm the image showed blue square with black center at top-left. Let me re-read: row1 = "WbbbW", row2 = "WbWbW", row3="WbbbW". So it's a blue 3x3 with white center. And the image shows a blue square with a dark center — the center is white? In the rendered image, the center appeared dark (maybe it's white rendered... no, white would be light). Hmm, in the image the top-left icon looks like a blue square with a small dark square in the center. Hmm.
Actually wait — in the ascii, the maze blue block at rows 8-12 cols 14-18: row10 = "WBbbBbbBBB" starting at col12: col12=W, col13=B, col14=b, col15=b, col16=B, col17=b, col18=b, col19=B. So the blue block has a black pixel at (10,16) — center. So the maze blue block is a 5x5 blue with black center. The legend is a 3x3 blue with white center.
Hmm, maybe the top-left items are legend: blue-with-hole icon = "the object to move"? gray square = ? And the small blue line = ?
Actually maybe top-left is a "goal indicator" panel showing the target shape, and the small bl
… [102 caracteres más]

```python
a = current_frame.ascii.split('\n')
def crop(r0,r1,c0,c1):
    for r in range(r0,r1+1):
        print(r, a[r][c0:c1+1])
crop(20,42,12,44)
print('---')
crop(42,57,12,52)
print('--- bottom rows')
crop(58,63,0,63)
```

```text
20 WBBBBBBBBBBBBBBBBBBBWWWWWWWBRBWWW
21 WBBBBBBBBBBBBBBBBBBBWWWWWWWBRBWWW
22 WBBBBBBBBBBBBBBBBBBBWWWWWWWBRBWWW
23 WBBBBBBBBBBBBBBBBBBBWWWWWWWBRBWWW
24 WBBBBBBBBBBBBBBBBBBBWWWWWWWBRBWWW
25 WBBBBBBBBBBBBBBBBBBBWWWWWWWBRBWWW
26 WBBBBBBBWWWWWWWWWWWWWWWWWWWBRBWWW
27 WBBBBBBBWWWWWWWWWWWWWWWWWWWBRBWWW
28 W
… [1698 caracteres más]
```

**Pensamiento:**

Let me reconstruct the maze layout. The maze area is rows 7-56, cols 13-51 roughly.
Structure:
- Blue 5x5 block with black center at rows 8-12, cols 14-18. This is likely the "player" (a pushable block? or the avatar).
- Red path: from (9,39)-(11,41) a 3x3 red block at top right, then a vertical red line down col 40 from row 12 to row 38, then a horizontal red line row 40 from col 19 to col 40, and a red 3x3 block at rows 38-42, col 13-18? Let's see: row 38: "WBRRRRRB" from col13: cols 14-18 red. row 39: "WBBRRRRBBB" cols 15-18. row40: "WBRRRRRRRRR..." cols 14-... So red forms a "path" drawn: a line from the red square at top-right going down and left to the red square at left (rows 38-42, cols 13-18 area). Hmm.
Actually the red seems to be a drawn path: red square at (9-11, 39-41) at top, line down col 40 rows 9..40, then along row 40 cols 14..40, and red square at rows 38-42 cols 14-18 (a plus-ish shape). Hmm.
- Bottom right: rows 48-56, cols 43-51: a blue structure: blue outline square (hollow) with a blue dot in the center: row 49: cols 43-49 blue; row 50: col 48 blue; ... row 52: col 43 blue and col 46 blue... Let me look at node 11: b 19 pixels bbox rows 49-55 cols 43-49, and node 12: b 1 pixel at (52,46). So the structure is a blue "C" shape (open ring) plus a center dot at (52,46). This is the goal: a target where the blue block should be placed? Like the blue square outline with center dot matching the blue block shape?
Hmm, the blue block at rows 8-12 cols 14-18 is 
… [3053 caracteres más]

```python
r = action(['UP'])
print(r)
d = frame_diff()
import json
print({k:(v if not isinstance(v,list) else v[:6]) for k,v in d.items() if k in ('changed_cell_count',)})
for k in ('moved','rotated','appeared','disappeared','changed_color','resized'):
    if d.get(k): print(k, json.dumps(d[k][:5]))
```

```text
[action] UP -> NO-OP (executed, no change inside the board area)
{'executed': True, 'action_num': 1, 'level': 1, 'score': 0, 'state': 'NOT_FINISHED', 'valid_actions': ['UP', 'DOWN', 'LEFT', 'RIGHT', 'SPACE'], 'board_changed': False, 'done': False, 'level_completed': False, 'game_over': False, 'run_c
… [221 caracteres más]
```

## Paso 2 · nivel 1 · acción 5

**Pensamiento:**

UP was a no-op. Let me test other directions individually to see what moves — but batching them all would confuse which moved. Let's try LEFT, DOWN, RIGHT one at a time with diffs, but each action costs a step. There's a step budget? time_remaining is large. The blue bar at row 63 full width — could be a step counter but it's full.
Let me try RIGHT then check diff; then DOWN; etc. Actually let me do them sequentially in one python call with diffs in between, since action() updates state immediately.
Careful: if a move actually moves the block, subsequent actions continue. Let me test each direction and record diff, then attempt to undo back. Simpler: try LEFT, record; then RIGHT, record; etc.
Let's write a loop: for each direction, do action, compute diff summary (changed cell count, moved components), print.

```python
import json
def summary(d):
    out = {'n': d['changed_cell_count']}
    for k in ('moved','appeared','disappeared','changed_color','resized'):
        v = d.get(k) or []
        if v:
            out[k] = [(e.get('color'), e.get('at_before') or e.get('at') or e.get('bbox'), e.get('at_after'), e.get('pixels')) for e in v][:4]
    return out

for act in ['LEFT','RIGHT','DOWN','UP']:
    r = action([act])
    d = frame_diff()
    print(act, r.get('no_op'), summary(d))
```

```text
[action] LEFT -> NO-OP (executed, no change inside the board area)
LEFT True {'n': 1, 'appeared': [('w', [63, 63], None, 1)], 'resized': [('b', [63, 0], [63, 0], None)]}
[action] RIGHT -> effect
RIGHT False {'n': 48, 'moved': [('b', None, None, 24), ('B', None, None, 1)], 'resized': [('B', [7, 13], 
… [261 caracteres más]
```

## Paso 3 · nivel 1 · acción 5

**Pensamiento:**

So RIGHT moved the blue block by some cells. The blue block moved from cols 14-18 to cols 20-24 (the white region at rows 14-18? no, it's still at rows 8-12 in the image... let me check).
Actually in the new image, the blue block appears at row ~8-12, col ~20-24. So it moved right by 6 cells? Hmm, the diff image shows changes at the top-left legend area (the legend item changed from blue-with-white-center to black-with-dark-center and a new blue icon appeared next to it?). Interesting — the legend at top-left changed: previously blue square with white center at (1,1)-(3,3) and gray at (1,5)-(3,7). Now: black square with dark center at (1,1)-(3,3) and blue with center at (1,5)-(3,7). So the legend "consumed"/shifted? Hmm, that's odd. Actually maybe the top-left is a palette/legend of remaining items.
Wait, maybe the top-left area is not a legend but a "queue" display. Hmm.
Let me just re-inspect the current segmentation and figure out the blue block's new position, and how far it moved with a single RIGHT (24 pixels moved + 1 black pixel). It moved from (8-12,14-18) to (8-12, 20-24)? Let's check.

```python
seg = current_frame.segmentation
for n in seg['nodes']:
    print(n['id'], n['color'], n['pixels'], n['boundary'][:4])
a = current_frame.ascii.split('\n')
print('--- legend')
for r in range(0,7): print(r, a[r][0:12])
print('--- block area')
for r in range(7,14): print(r, a[r][13:45])
```

```text
0 W 2649 [[0, 0], [0, 63], [62, 63], [62, 0]]
1 b 8 [[1, 1], [1, 3], [3, 3], [3, 1]]
2 w 9 [[1, 5], [1, 7], [3, 7], [3, 5]]
3 W 1 [[2, 2]]
4 b 3 [[5, 1], [5, 3]]
5 B 879 [[7, 13], [7, 43], [13, 43], [13, 42]]
6 b 24 [[8, 20], [8, 24], [12, 24], [12, 20]]
7 R 82 [[9, 39], [9, 41], [11, 41], [12, 40]]
… [618 caracteres más]
```

**Pensamiento:**

The blue block moved from cols 14-18 to cols 20-24 — i.e., it slid 6 cells right, from the start position to... hmm, it slid until blocked? The corridor: at row 8-12, cols 14-18 was the start (blue on white? actually the block sits on white floor presumably). Moving right it went to cols 20-24, then col 25 is B wall. So it slid until hitting a wall — like an ice-sliding puzzle (slippery, move until blocked)!
Wait, but the block moved 6 cells: from 14-18 to 20-24, so it slid right until the wall at col 25. Yes! Ice-slide mechanics: press a direction, block slides until it hits an obstacle.
Hmm, but is it sliding until blocked, or just moving by 6? Let me check the maze floor structure. Actually the block started at rows 8-12 cols 14-18 which is at the top-left corner of the maze. Up and Left were no-ops (already at wall). Down was no-op — hmm, that's odd: if it can slide down, from rows 8-12 at cols 14-18, going down it should slide to the bottom... but Down was a no-op. Let me check the maze below the start: rows 13, cols 14-18: row 13 was "BBBBBBBB..." at cols 13-... so there's a wall right below. And the white region at rows 14-18 cols 20-24 is below-right of the block. Hmm, so the block at cols 20-24 rows 8-12, below it at rows 14-18 cols 20-24 is white (node 9). Wait row 13 col 20-24: from row 13 printed above (cols 13-45): "BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBW" → all B. So below the block at cols 20-24 is a wall at row 13. So Down would be no-op now. Earlier at cols 14-18, b
… [8180 caracteres más]

```python
a = current_frame.ascii.split('\n')
# exact cell inventory by color
from collections import defaultdict
cells = defaultdict(list)
for r,row in enumerate(a):
    for c,ch in enumerate(row):
        cells[ch].append((r,c))
for k,v in cells.items():
    print(k, len(v))
# red cells
red = sorted(cells['R'])
print('red bbox', red[0][0], red[0][1], red[-1][0], red[-1][1])
# print red shape as set rows
rows = sorted(set(r for r,c in red))
for r in rows:
    cs = [c for rr,c in red if rr==r]
    print(r, cs)
```

```text
W 3006
b 117
w 11
B 880
R 82
red bbox 9 39 42 18
9 [39, 40, 41]
10 [39, 40, 41]
11 [39, 40, 41]
12 [40]
13 [40]
14 [40]
15 [40]
16 [40]
17 [40]
18 [40]
19 [40]
20 [40]
21 [40]
22 [40]
23 [40]
24 [40]
25 [40]
26 [40]
27 [40]
28 [40]
29 [40]
30 [40]
31 [40]
32 [40]
33 [40]
34 [40]
35 [40]
36 [40]
37 [
… [211 caracteres más]
```

## Paso 3 · nivel 1 · acción 8

**Pensamiento:**

Now let me build the maze model. Let me get the walkable map (W and R cells inside the maze) and the block shape (5x5 with center hole showing black — the center black pixel is part of the block? The block is 24 blue pixels + 1 black center = 25 cells, i.e., a 5x5 with a black center dot).
Now, the maze structure. Let me build a grid of the maze region and print a compact map with symbols, marking floor (W or R) vs wall (B) vs block (b) vs target.
Let me print the maze region rows 7..57, cols 13..52 as a compact map where I map: B -> '#', W -> '.', R -> 'r', b -> 'b'.
That's 51 rows x 40 chars = manageable but big-ish. Let me instead compute connectivity programmatically. But I also want to see it. Let me print it — 51 lines of 40 chars is fine (about 2000 tokens). Actually let's compress: print with run-length? Better: just print, it's important.
Actually, let me be smarter: compute the block's valid positions via BFS with slide mechanics, and also render the map compactly.
Key question: is red floor walkable by the block? The red corridor is 1-wide so the block can't enter it anyway (block is 5 wide). But the red blobs (3x3 at top, cross at left) also can't fit a 5x5 block... The cross shape at rows 38-42 cols 14-18 is 5x5 minus cells (39,14) and (41,14). Hmm interesting: that's exactly a 5x5 area with 2 cells missing at the left edge — the block couldn't be there fully.
Wait... maybe the red is a *trail* left by the blue block in a previous demo? Or maybe the red is a "sna
… [2776 caracteres más]

```python
f0 = history[0].frame
g0 = f0.ascii.split('\n')
blue_bottom = [(r,c) for r in range(45,58) for c in range(40,54) if g0[r][c]=='b']
print('target cells', blue_bottom)
# maze map
def cellmap(g,r,c): return g[r][c]
lines=[]
for r in range(7,57):
    row = ''.join('#' if g0[r][c]=='B' else ('.' if g0[r][c]=='W' else ('r' if g0[r][c]=='R' else ('b' if g0[r][c]=='b' else '?'))) for c in range(13,53))
    lines.append(f'{r:2d} {row}')
print('\n'.join(lines))
```

```text
target cells [(49, 43), (49, 44), (49, 45), (49, 46), (49, 47), (49, 48), (49, 49), (50, 49), (51, 49), (52, 46), (52, 49), (53, 49), (54, 49), (55, 43), (55, 44), (55, 45), (55, 46), (55, 47), (55, 48), (55, 49)]
 7 ###############################.........
 8 #bbbbb#########################........
… [2113 caracteres más]
```

**Pensamiento:**

Now I see the maze (cols 13..52 shown). The maze interior:
- Start: block at rows 8-12, cols 14-18 (relative col 1-5 in this crop).
- Corridor at rows 14-18, cols 20-24 (crop cols 7-11) — a 5x5 pocket.
- Corridor rows 14-18, cols 32-38 (crop cols 19-25) — 7 wide, 5 tall.
- Rows 19-25: cols 32-38 open.
- Rows 26-37: cols 20-38 open (crop cols 7-25).
- Col 40 rows 12-38: 1-wide red corridor (crop col 27).
- Row 40: cols 14-40 red corridor (1 tall).
- Rows 42-47: cols 20-... open (crop cols 7+): row 42 crop shows "#rrrrr#................" so cols 20-43 open at row 42? Actually crop col 7 = col 20. Row 42: cols 14-18 red, col 19 '#', cols 20-52 open (dots).
- Rows 43-47: cols 20-42 open (crop cols 7-29), then cols 43-52 dots too? Row 43: "#######................................." → crop cols 7-40 are dots = cols 20-53 open. Hmm, but the maze boundary is at col 51? Row 48: "#######......................#########.." → crop cols 7-32 dots (cols 20-45 open), then crop cols 33-41 = '#' → cols 46-54 are '#'. Hmm wait.
Let me recompute: crop col index i corresponds to actual col 13+i. Row 48 string: '#######......................#########..' → positions 0-6 = '#' (cols 13-19), 7-32 = '.' (cols 20-45), 33-41 = '#' (cols 46-54), 42-43='.' (cols 55-56).
Hmm, that doesn't match the earlier observation that the target ring is at rows 49-55, cols 43-49. Row 49: '##############################bbbbbbb#..' → positions 0-29 = '#' (cols 13-42), positions 30-36 = 'b' (cols 43-49), position 37 = '#'
… [18771 caracteres más]

```python
def blockpos(g):
    cs = [(r,c) for r in range(64) for c in range(64) if g[r][c]=='b']
    if not cs: return None
    rs=[p[0] for p in cs]; c2=[p[1] for p in cs]
    return (min(rs),max(rs),min(c2),max(c2),len(cs))
g = current_frame.ascii.split('\n')
print('before', blockpos(g))
for i in range(3):
    r = action(['RIGHT'])
    g = current_frame.ascii.split('\n')
    print(i, 'no_op' if r.get('no_op') else 'moved', blockpos(g))
```

```text
before (1, 63, 0, 61, 117)
[action] RIGHT -> effect
0 moved (1, 63, 0, 60, 116)
[action] RIGHT -> effect
1 moved (1, 63, 0, 60, 116)
[action] RIGHT -> effect
2 moved (1, 63, 0, 59, 115)
```

## Paso 4 · nivel 1 · acción 9

**Pensamiento:**

Very interesting! The animation timeline says 27 cells changed and changed back around rows 8-42, cols 19-40. That's the red trail region! So the red trail flashes/recomputes.
Also the diff image shows the red blob changed shape (now at rows 38-42, cols 15-18 or so).
Let me now check the current state: the block position and the red trail.
The block is now at the top-right (rows 8-12, cols 37-41?). Let me check.
Also the red trail seems to have changed: the red vertical line at col 40 disappeared? In the current image, the red line is still there from the block's bottom to the bottom-left. Hmm.
Let me get a precise current picture: block position, red cells.
Key insight forming: maybe the red trail is the *path the block has traveled* (like a snake body) — the trail is drawn from where the block has been! Initially the trail existed from the top-right down to the left — that could be from a previous level/demo? Hmm.
Actually wait! Maybe the red trail is a "laser" that shoots from the block's *starting* position? Or maybe the red trail is the *ghost path* showing where the block will go?
Let me look at the diff image more carefully: changes are at top-left (block's old position now black), the block's new position (top right, blue), and around rows 38-42 cols 14-18 the red blob changed shape (some red cells disappeared on the left, some appeared on the right).
So each RIGHT press: the block moves right, and the red blob at rows 38-42 cols 14-18 shifts?? That's bizarre... unles
… [794 caracteres más]

```python
g = current_frame.ascii.split('\n')
blue = [(r,c) for r in range(64) for c in range(64) if g[r][c]=='b' and r>6]
red = [(r,c) for r in range(64) for c in range(64) if g[r][c]=='R']
print('blue', min(r for r,c in blue), max(r for r,c in blue), min(c for r,c in blue), max(c for r,c in blue), len(blue))
rows = sorted(set(r for r,c in red))
for r in rows:
    print('R', r, [c for rr,c in red if rr==r])
print('timeline:')
tl = last_animation_timeline
for s in tl['steps'][:14]:
    print(s.get('step'), s.get('bbox'), str(s.get('changes'))[:150])
```

```text
blue 8 63 0 59 104
R 13 [40]
R 14 [40]
R 15 [40]
R 16 [40]
R 17 [40]
R 18 [40]
R 19 [40]
R 20 [40]
R 21 [40]
R 22 [40]
R 23 [40]
R 24 [40]
R 25 [40]
R 26 [40]
R 27 [40]
R 28 [40]
R 29 [40]
R 30 [40]
R 31 [40]
R 32 [40]
R 33 [40]
R 34 [40]
R 35 [40]
R 36 [40]
R 37 [40]
R 38 [20, 21, 22, 23, 24, 40]
R
… [1354 caracteres más]
```

**Pensamiento:**

Now I understand better! The block moved right by 6 (step by step animation, 6 steps), and simultaneously the red blob at rows 38-42 cols 14-18 moved right by 6 (to cols 20-24)! So the red blob is a SECOND object that moves in lockstep with the blue block!
Wait, look at step 8-13: the red blob at rows 38-42 shifted right from cols 14-18 to cols 20-24. And the red trail: the red trail's left part is now shorter — the red horizontal line at row 40 now goes from col 20 to col 40 (previously col 14 to 40). And the red vertical line at col 40 now starts at row 13 (previously row 12) — hmm, the top of the vertical line: the red 3x3 at rows 9-11 cols 39-41 is GONE (the blue block covered it!). The block slid over the red 3x3 and consumed it!
So: the red trail is a *trail* left by the red blob? No wait. Let me think again.
New model: There are TWO objects: the blue block (5x5) and a red block (5x5-ish). Both move with the same arrow keys? Hmm, but the red blob at rows 38-42 cols 14-18 moved right 6, exactly like the blue block moved right 6. So they both move together.
And the red trail = the *history* of the red blob's positions? No, the trail is 1-wide.
Hmm, actually, maybe the red trail is the path the red blob traveled: the red blob started at the top-right (the red 3x3 at rows 9-11 cols 39-41)? and traveled down col 40 and left along row 40 to the left side... but the trail is 1-wide, so the trail marks the *center* of the red blob? No, the trail is 1-wide but the blob is 5x5.
H
… [19060 caracteres más]

```python
def objs(g):
    blue = [(r,c) for r in range(6,62) for c in range(64) if g[r][c]=='b']
    red = [(r,c) for r in range(6,62) for c in range(64) if g[r][c]=='R']
    def bb(cs):
        if not cs: return None
        rs=[p[0] for p in cs]; cc=[p[1] for p in cs]
        return (min(rs),max(rs),min(cc),max(cc),len(cs))
    return bb(blue), bb(red)
g = current_frame.ascii.split('\n')
print('cur', objs(g))
r = action(['DOWN'])
print('down no_op?', r.get('no_op'))
g2 = current_frame.ascii.split('\n')
print('after', objs(g2))
d = frame_diff()
print(summary(d))
```

```text
cur ((8, 55, 38, 49, 44), (13, 42, 20, 40, 66))
[action] DOWN -> NO-OP (executed, no change inside the board area)
down no_op? True
after ((8, 55, 38, 49, 44), (13, 42, 20, 40, 66))
{'n': 0}
```

## Paso 5 · nivel 1 · acción 9

**Pensamiento:**

DOWN was a no-op. The blue block is at rows 8-12 cols 38-42 (the bbox includes the target ring: (8,55,38,49) since blue includes the target). The red is at rows 13-42 cols 20-40 (the trail + blob).
So DOWN from rows 8-12 cols 38-42 was blocked. Under "slide until blocked by white", the block could move down 1 (row 13 cols 38-42 = black/red). It didn't. Under "exactly 6 cells or nothing": destination rows 14-18 cols 38-42 contains white → blocked ✓.
So the model is: the block moves exactly 6 cells per press (if the destination footprint is all non-white? or all black/red?), else no-op.
Hmm, wait. Is 6 the right number? Let me reconsider: maybe the block moves exactly 6 cells... but why 6? Hmm, maybe the block moves until it's aligned with a grid of period 6? Or maybe the block's movement is "slide until the cell 6 ahead..."? Hmm.
Alternatively: maybe the block moves until blocked, but the "blockers" are the *white corridors* extended as full rows/columns? Like the white corridors act as "gaps" that the block can't cross, and the block stops *before* being adjacent? Hmm.
Let me reconsider the first RIGHT: from cols 14-18 to 20-24. What white is at cols 25-29 in rows 8-12? None. Hmm, but what if the block stops when it reaches a position where it could then go down (a "junction")? At cols 20-24, below is the white pocket... but the block can't go down there (blocked).
Hmm, what about the red blob? The red blob also moved exactly 6. And the red blob is a 5x5 blob whose "movement"
… [11325 caracteres más]

```python
def blob(g):
    # red 5x5-ish blob = red cells in rows 36-44
    cs = [(r,c) for r in range(36,45) for c in range(64) if g[r][c]=='R']
    if not cs: return None
    rs=[p[0] for p in cs]; cc=[p[1] for p in cs]
    return (min(rs),max(rs),min(cc),max(cc),len(cs))
def blk(g):
    cs = [(r,c) for r in range(6,46) for c in range(64) if g[r][c]=='b']
    if not cs: return None
    rs=[p[0] for p in cs]; cc=[p[1] for p in cs]
    return (min(rs),max(rs),min(cc),max(cc),len(cs))
for i,h in enumerate(history):
    g = h.frame.ascii.split('\n')
    print(i, h.action, 'blob', blob(g), 'blk', blk(g))
```

```text
0  blob (36, 42, 14, 40, 49) blk (8, 12, 14, 18, 24)
1 UP blob (36, 42, 14, 40, 49) blk (8, 12, 14, 18, 24)
2 LEFT blob (36, 42, 14, 40, 49) blk (8, 12, 14, 18, 24)
3 RIGHT blob (36, 42, 14, 40, 49) blk (8, 12, 20, 24, 24)
4 DOWN blob (36, 42, 14, 40, 49) blk (8, 12, 20, 24, 24)
5 UP blob (36, 42, 1
… [265 caracteres más]
```

## Paso 5 · nivel 1 · acción 18

**Pensamiento:**

Key data: the red blob (rows 38-42 cols 14-18) moved right by 6 only on the 4th RIGHT press (index 8), i.e., after the blue block had moved 4 presses right. Hmm, actually it moved on press index 8 which was the 4th RIGHT.
Hmm, what's special? On press 8, the blue block reached cols 38-42 and consumed the red 3x3 marker. Maybe the red blob moves when the blue block *reaches the end of its travel* (i.e., when the blue block's move is blocked)? No, press 6 and 7 also moved the blue 6 cells each.
Hmm, maybe the red blob moves every 4th press? Or maybe the red blob moves when the blue block's footprint overlaps a red cell? Press 8: the blue block moved into cols 38-42, overlapping the red 3x3 at cols 39-41 rows 9-11 ✓. On presses 3, 6, 7 the blue block didn't overlap red cells (the red trail is at col 40 rows 12-38 and row 40 cols 14-40; the blue is at rows 8-12; the trail cell (12,40) — on press 8 the blue block covered (12,40)? The blue block's footprint rows 8-12 cols 38-42 includes (12,40) which was red ✓ (the timeline showed 'R>b @ (12,40)').
So hypothesis: the red blob moves when the blue block touches/overlaps the red trail. Hmm, but that seems odd too.
Alternative hypothesis: the red blob moves when the blue block's move *stops against a wall*? Press 8 ended at cols 38-42 with white at col 43 → blocked. Presses 3, 6, 7 ended with black ahead (not blocked). So the red blob moves only when the blue block's slide is blocked by a wall! That would be consistent with "slide" mec
… [3315 caracteres más]

```python
g = current_frame.ascii.split('\n')
R,C = 64,64
def passable(r,c):
    if r<0 or c<0 or r>=R or c>=C: return False
    ch = g[r][c]
    if ch in 'Ww': return False
    return True
# block footprint 5x5 passable check
def ok(r,c):
    if not (0<=r and r+4<R and 0<=c and c+4<C): return False
    for rr in range(r,r+5):
        for cc in range(c,c+5):
            if not passable(rr,cc): return False
    return True
start = (8,38)
goal = (50,44)
print('start ok', ok(*start), 'goal ok', ok(*goal))
from collections import deque
D = {'U':(-6,0),'D':(6,0),'L':(0,-6),'R':(0,6)}
prev = {start: None}
q = deque([start])
while q:
    s = q.popleft()
    if s == goal: break
    for k,(dr,dc) in D.items():
        n = (s[0]+dr, s[1]+dc)
        if n not in prev and ok(*n):
            prev[n] = (s,k)
   
… [311 caracteres más]
```

```text
start ok True goal ok True
reached goal True
len 16 LLDDLLDDDDDRRRRR
reachable count 21
[(8, 14), (8, 20), (8, 26), (8, 32), (8, 38), (14, 14), (14, 26), (20, 14), (20, 20), (20, 26), (26, 14), (32, 14), (38, 14), (38, 20), (44, 14), (50, 14), (50, 20), (50, 26), (50, 32), (50, 38), (50, 44)]
```

**Pensamiento:**

A 16-move path exists: LLDDLLDDDDDRRRRR from the current position. Total from the start would be 20 moves. But I've already used 10 steps (some wasted). Is there a step limit? The bottom bar (row 63) is a blue bar that shrinks — it's at cols 0-59 now (was 0-63). So the budget is 64 - something. Let me check: initially row 63 had 64 blue cells; after 4 actions it had 62; now after ~10 actions... Let me check the current bar length. Earlier: node 13 b 64 → after 1 action b 62 + w 2? Hmm, at step 6 the bar was b 62 (cols 0-61) + w 2. Then after 3 more RIGHTs, it's b 59 (cols 0-59)? The last objs showed blue max col 59 for row 63. So the bar shrinks 1 cell per action → 64 actions total budget? We've used 10, so 54 left. The path needs 16. Fine.
Wait, but the bar might be a level-wide timer. Let's just move efficiently.
Actually, hold on. Before executing 16 moves, let me double check the model with a small probe: the first move of the path is L (from (8,38) to (8,32)). Let me batch the whole path and check the result at the end. If the model is right, we reach the goal in 16 moves. Risk: if the model is wrong, the block ends up somewhere unexpected but recoverable (the maze is small).
Actually, let me be smarter: batch a few moves at a time and verify. First batch: 'LLDD' (4 moves) and verify positions. Actually let me batch the whole thing but verify with blk() after each move inside the loop, and stop if a move is a no-op. That's safer and efficient.
Let me write a loop that ex
… [402 caracteres más]

```python
path = 'LLDDLLDDDDDRRRRR'
m = {'U':'UP','D':'DOWN','L':'LEFT','R':'RIGHT'}
expected = {'L':(0,-6),'R':(0,6),'U':(-6,0),'D':(6,0)}
cur = (8,38)
log=[]
for k in path:
    r = action([m[k]])
    g = current_frame.ascii.split('\n')
    b = blk(g)
    pos = (b[0], b[2]) if b else None
    exp = (cur[0]+expected[k][0], cur[1]+expected[k][1])
    log.append(f'{k} no_op={bool(r.get("no_op"))} at={pos} exp={exp} lvl={r.get("level")} done={r.get("done")} lc={r.get("level_completed")} go={r.get("game_over")}')
    if pos != exp or r.get('level_completed') or r.get('game_over') or r.get('done'):
        break
    cur = pos
print('\n'.join(log[-6:]))
print('last pos', cur)
```

```text
[action] LEFT -> effect
[action] LEFT -> effect
[action] DOWN -> effect
[action] DOWN -> effect
[action] LEFT -> effect
[action] LEFT -> effect
[action] DOWN -> effect
[action] DOWN -> effect
[action] DOWN -> NO-OP (executed, no change inside the board area)
D no_op=False at=(20, 26) exp=(20, 26) lv
… [419 caracteres más]
```

## Paso 6 · nivel 1 · acción 18

**Pensamiento:**

Interesting developments:
1. The block is now at (32,14) — rows 32-36, cols 14-18. The DOWN to (38,14) was a no-op. Why? Because the red blob is at rows 38-42, cols 14-18! The red blob moved back left to cols 14-18 (as seen in the diff image, the red blob is at cols 14-18 now and the trail retracted). So the RED BLOB IS AN OBSTACLE blocking the blue block!
Also, the red 3x3 marker at the top-right has REAPPEARED (the diff image shows red at top-right rows 9-11 cols 39-41). Wait, the diff image shows a red square at the top-right (~row 10, col 40) in true color = changed. So the red marker came back! Interesting — the red thing restored it.
So the red is a *snake*: head = 5x5 blob, body = 1-wide trail, and the "head" moves along the trail path. The trail's far end (the 3x3) is where the snake's tail is? Hmm.
Let me reconsider: The red snake's path: the 3x3 at (9-11, 39-41) is one end, then down col 40, then left along row 40 to the blob at cols 14-18 (the other end). The blob is the "head" at one end of the path.
Observation: the blob moved right by 6 (to cols 20-24) at press 8, and now it's back at cols 14-18. So the blob oscillates? It moved right 6 when the blue block consumed the 3x3 marker at the other end of the trail, and now it moved back left?
Hmm, let me look at the current state precisely. Let me get the red cells now and the block position.
Actually, the key insight: the red blob blocks the blue block's movement (DOWN to (38,14) was a no-op). So the red blob is an 
… [3369 caracteres más]

```python
def redinfo(g):
    cs = [(r,c) for r in range(6,62) for c in range(64) if g[r][c]=='R']
    marker = (9,39) in cs or (10,40) in cs
    blobc = [(r,c) for r,c in cs if r>=36]
    vert = [(r,c) for r,c in cs if c==40 and r<36]
    horz = [(r,c) for r,c in cs if r==40]
    bl = None
    if blobc:
        rs=[p[0] for p in blobc]; cc=[p[1] for p in blobc]
        bl=(min(rs),max(rs),min(cc),max(cc))
    return dict(marker=marker, blob=bl, vertlen=len(vert), horz=(min([c for r,c in horz]),max([c for r,c in horz])) if horz else None, n=len(cs))
for i,h in enumerate(history):
    print(i, h.action, redinfo(h.frame.ascii.split('\n')))
```

```text
0  {'marker': True, 'blob': (36, 42, 14, 40), 'vertlen': 27, 'horz': (14, 40), 'n': 82}
1 UP {'marker': True, 'blob': (36, 42, 14, 40), 'vertlen': 27, 'horz': (14, 40), 'n': 82}
2 LEFT {'marker': True, 'blob': (36, 42, 14, 40), 'vertlen': 27, 'horz': (14, 40), 'n': 82}
3 RIGHT {'marker': True, 'blob
… [1454 caracteres más]
```

**Pensamiento:**

Very interesting! The red configuration changed ONLY at press 8 and reverted at press 10 (the first LEFT after that). At press 9 (DOWN, a no-op) nothing changed.
Press 8 = RIGHT, block moved from cols 32-36 to 38-42, overlapping the red marker (rows 9-11 cols 39-41) and the trail's top cell (12,40). Result: the marker disappeared, the blob moved right 6, the trail's horizontal part lost its leftmost 6 cells (now cols 20-40), and the vertlen decreased from 27 to 23 (4 fewer: rows 9,10,11,12 at col 40 were consumed by the blue block: (12,40) red, and (9,40),(10,40),(11,40) were part of the marker).
Press 10 = LEFT, block moved from (8,38) to (8,32): everything reverted to the original (marker back, blob back at cols 14-18, trail full).
So the red "snake" is not an independent moving object — it's a *rendering* that depends on the blue block's position! Specifically, the red trail is drawn as the path from the blue block's current position to the target?? Hmm no.
Let me think: the red is a "route" that is computed relative to the blue block's position. When the block is at cols 38-42 (rows 8-12), the red trail = the route from the block's position to the blob's position? Hmm.
Alternative: the red is a *pipe/laser path* that connects the block's current position to the red blob, i.e., the red is drawn as a path from the blue block to a fixed red target at rows 38-42 cols 14-18. Let me test this hypothesis:
- When the block was at cols 14-18 (rows 8-12) initially, the red path was
… [35006 caracteres más]

## Paso 6 · nivel 1 · acción 19

**Pensamiento:**

Let me re-derive the maze structure (black = passable, white = wall) and the reachable position grid, so I can see where the block can go and where the head blocks.
Let me compute the passable grid for 5x5 footprints at positions with rows/cols ≡ start mod 6, and print a compact map.
Also, let me reconsider the red head's behavior once more. New idea: maybe the head's position depends on the block's position via "the red path has fixed total length and is drawn as the shortest route from the block's center to the head"? Hmm.
Let me test the hypothesis: "the red path connects the block's current position to the head, routed through the maze, with a fixed length". Initially: block center (10,16), path: 3x3 at (10,40) → down col 40 → left row 40 → head center (40,16). The path's start (10,40) is not the block's center.
Hmm, what if the path connects the *target* to the head? The target center is (52,46). No.
What if the red thing is a "laser" that the block must dodge... 
Honestly, let me test the drag hypothesis directly with a cheap experiment. But first let me map the reachable positions to know my options.
Actually, here's an important new thought: maybe the head's movement isn't caused by the block at all, but by the *step counter* — e.g., the head moves one step every 4 steps along a patrol route, and the timing coincidentally matched. Data: head moved at history index 8 and index 10 (steps 8 and 10). If it moved every 2 steps starting at 8, it would move at 12, 14, 16, 18
… [1102 caracteres más]

```python
g = current_frame.ascii.split('\n')
def passable_ch(ch): return ch not in 'Ww'
def ok(r,c,g=g):
    if not (0<=r and r+4<64 and 0<=c and c+4<64): return False
    return all(passable_ch(g[rr][cc]) for rr in range(r,r+5) for cc in range(c,c+5))
def redcells(g=g):
    return set((r,c) for r in range(6,62) for c in range(64) if g[r][c]=='R')
def headcells(g=g):
    # head = red cells within rows 37-43, cols blob
    rc = redcells(g)
    blobc = [(r,c) for (r,c) in rc if 37<=r<=43]
    if not blobc: return set()
    cmin = min(c for r,c in blobc)
    return set((r,c) for r in range(38,43) for c in range(cmin,cmin+5))
from collections import deque
start=(32,14)
D={'U':(-6,0),'D':(6,0),'L':(0,-6),'R':(0,6)}
seen={start}; q=deque([start])
while q:
    s=q.popleft()
    for k,(dr,dc) in D.items():
… [362 caracteres más]
```

```text
reachable 20 [(8, 14), (8, 20), (8, 26), (8, 32), (8, 38), (14, 14), (14, 26), (20, 14), (20, 20), (20, 26), (26, 14), (32, 14), (38, 14), (44, 14), (50, 14), (50, 20), (50, 26), (50, 32), (50, 38), (50, 44)]
overlap-red positions [(8, 38), (38, 14)]
head left col 14 goal ok True
```

**Pensamiento:**

Confirmed: only two positions overlap red: (8,38) and (38,14). (38,14) is where the head is (blocked).
So the only "drag" position is (8,38). And from (8,38), the only possible move is LEFT, which drags the head LEFT (already at its left limit).
Hmm. So the drag mechanic can't move the head right. So my model must be wrong, OR the intended solution involves something else.
Let me reconsider. What if the head moves on its own and the correlation is coincidental? Let me reconsider the timing: the head moved during press 8's animation and during press 10's animation.
Hmm, what if the head moves based on the number of *steps taken* by the block (distance traveled)? The block's total distance: press 3: +6 (total 6); press 6: +6 (12); press 7: +6 (18); press 8: +6 (24) → head moved! press 9: 0 (24); press 10: +6 (30) → head moved! press 11: +6 (36); press 12: +6 (42); ... no head movement. Hmm, if the head moved every 24 units... 24 and 30, no.
What if the head moves every 4th *successful* block move? Successful moves: #1 press3, #2 press6, #3 press7, #4 press8 (head moved ✓), #5 press10 (head moved ✗ should be #8).
What if the head moves when the block's move count since the last head move ≥ ... press8 and press10 are 2 apart. Then 12, 14, ... no.
Hmm, what if the head moves based on the block's *position parity*? Or the head moves toward/away from the block when the block is within some distance?
Let me reconsider: maybe the head's position is a function of the block's position a
… [5427 caracteres más]

```python
r = action(['SPACE'])
print('space no_op?', r.get('no_op'), r.get('level_completed'), r.get('game_over'))
g = current_frame.ascii.split('\n')
print('blk', blk(g), 'red', redinfo(g))
d = frame_diff()
print(summary(d))
```

```text
[action] SPACE -> effect
space no_op? False False False
blk (8, 12, 14, 18, 24) red {'marker': True, 'blob': (36, 42, 14, 40), 'vertlen': 27, 'horz': (14, 40), 'n': 82}
{'n': 71, 'moved': [('b', None, None, 8), ('b', None, None, 3), ('b', None, None, 24), ('B', None, None, 1)], 'appeared': [('W', [2
… [154 caracteres más]
```

## Paso 7 · nivel 1 · acción 19

**Pensamiento:**

SPACE = RESET/RESTART! The block is back at (8,14) — the initial position! The animation showed 274 cells changing. The legend changed too: now the gray icon is at (1,1) and the blue icon at (1,5), and the small bar moved from (5,1) to (5,5)? The legend items swapped positions.
Hmm, so SPACE is a "restart/undo" that returns the block to its start. The legend at the top-left seems to be a "history/undo stack" indicator! The gray square + blue square + small bars... Actually, maybe the top-left shows the "reset" button icon.
Wait, look at the diff: the blue block moved from (32,14) back to (8,14). So SPACE = reset the block to the start. The red snake is unchanged (still at cols 14-18 with the full trail).
Hmm, but interestingly the legend at the top-left changed: previously [blue-ring icon at (1,1)-(3,3), gray at (1,5)-(3,7), small blue bar at (5,1)-(5,3)]. Now: gray at (1,1), blue at (1,5), white bar at (5,1), blue bar at (5,5). So the legend elements swapped. This looks like a "two-state toggle" indicator. Hmm, maybe the legend indicates which object you control?! 
OH WAIT. Maybe this is a game where you switch between controlling two objects! The legend shows two icons: a blue block icon and a gray block icon. Pressing SPACE switches control between the blue block and... something (gray = the red head?). Hmm, the animation showed 274 cells changing over rows 5-43 cols 4-42 — that includes the block teleporting from (32,14) to (8,14)... 
Hmm, actually maybe SPACE didn't rese
… [681 caracteres más]

```python
tl = last_animation_timeline
print(tl['action'], len(tl['steps']))
for s in tl['steps']:
    ch = s.get('changes')
    print(s['step'], s['bbox'], (str(ch)[:110] if ch else s.get('transitions')))
```

```text
SPACE 17
1 rows 26-36, cols 14-18 {'B>b': 24, 'b>B': 24}
2 rows 20-30, cols 14-18 {'B>b': 24, 'b>B': 24}
3 rows 20-24, cols 14-24 {'b>B': 24, 'B>b': 24}
4 rows 20-24, cols 20-30 {'b>B': 24, 'B>b': 24}
5 rows 14-24, cols 26-30 {'B>b': 24, 'b>B': 24}
6 rows 8-18, cols 26-30 {'B>b': 24, 'b>B': 24}
7 ro
… [715 caracteres más]
```

**Pensamiento:**

Fascinating! The SPACE animation shows the block *replaying* its entire path: frames 1-8 show the block moving from (32,14) up and right to (8,38) — i.e., replaying my moves in order?? Let me trace: frame 1: block at rows 26-30 (moved up from 32), frame 2: rows 20-24, frame 3: rows 20-24 cols 20-24? Hmm, frame 3's bbox is rows 20-24 cols 20-30 with 'b>B' at cols 20-24 and 'B>b' at cols 26-30 → the block moved right from (20,20)?? Hmm, that's not my move order.
Actually the replay seems to be: the block retraces the path from the current position back to the start, in reverse: (32,14) → (26,14) → (20,14) → (20,20)? Hmm, frame 3 shows the block moving from cols 26-30 to 20-24 at rows 20-24, i.e., moving LEFT from (20,26) to (20,20). So the replay path was (32,14) → (26,14) → (20,14) → (20,20)?? no...
Hmm, the replay path: 32,14 → 26,14 → 20,14 → 20,20 → 20,26 → 14,26 → 8,26 → 8,32 → 8,38 → (frame 9-10: the red snake reverts, the trail disappears?) → 8,32 → 8,26 → 8,20 → 8,14 (frames 11-13).
Hmm, that's odd. Frames 1-8: the block goes UP from (32,14) to (20,14), then RIGHT to (20,26), then UP to (8,26), then RIGHT to (8,38). That's the *forward* path from the start! Wait no — my actual path from the start was: (8,14)→(8,20)→(8,26)→(8,32)→(8,38)→(8,32)→(8,26)→(20,26)→(20,20)→(20,14)→(26,14)→(32,14). Reversed: (32,14)→(26,14)→(20,14)→(20,20)→(20,26)→(14,26)... hmm, but the frames show the block at (20,14)→(20,20)→(20,26)→(14,26)→(8,26)→(8,32)→(8,38). Yes! That IS the reverse of my
… [36506 caracteres más]

## Paso 7 · nivel 1 · acción 19

**Pensamiento:**

Interesting: the HUD now shows: gray icon at (1,1)-(3,3), blue-ring icon at (1,5)-(3,7), and the small bar at (5,4)-(5,6) (blue). 
Wait, look at the current image: top-left shows a gray square at (1,1), a blue square at (1,5), and a blue bar at (5,4)-(5,6) (below the blue square). So the bar is under the blue icon.
Hypothesis: the top-left is a "two-slot" display: the blue block icon and a gray icon. The bar under the blue icon = a counter? Hmm.
Hmm, what if the gray icon is the *level counter* or a "second block" indicator? 
Let me reconsider the HUD: maybe the HUD is a "goal indicator" showing: [gray square] [blue square] = the two objects, and the bar = progress.
Actually, maybe the HUD icons represent the *legend*: blue = the block you control, gray = the wall? And the bar = the step budget for the level?
Hmm, the bar moved right by 3 after SPACE. If the bar were a budget counter, it would shrink, not move.
Let me now think about the level differently. Let me look at the whole board image again with fresh eyes:
- A black maze with white walls (inverted colors from typical).
- Blue 5x5 block at the top-left of the maze.
- A red 3x3 at the top-right, with a red line going down and left, ending in a red 5x5 blob at the left-middle.
- A blue target ring at the bottom-right.
The red path: from the red 3x3 (top-right) → down → left → to the red blob. The red blob is at the corridor that leads down to the target. So the red path is like a "route" from the top-right to the corrid
… [35614 caracteres más]

## Paso 7 · nivel 1 · acción 19

**Pensamiento:**

I'm at (8,14) after the SPACE rewind. Budget: the bottom bar — let me check its length to know remaining steps.
Let me design a decisive experiment with a batch:
Plan A: Test whether the red head is an obstacle or whether the underlying terrain at rows 38-42 cols 14-18 is white (wall). 
Key insight for a cheap test: move the block to (8,38) (4 RIGHTs) so the head moves to cols 20-24, then immediately press LEFT... no.
Hmm, better idea: the head's position depends on the block's col. The head is at cols 20-24 when the block is at (8,38). What if I then move the block LEFT to (8,32) and DOWN... no.
Hmm, what about this: the head at (38,20) occupies rows 38-42 cols 20-24. If the head is at cols 20-24, then the trail's horizontal part spans cols 20-40 at row 40 (the cells cols 14-19 became black). So the cells (38..42, 14..18) became black (passable?) — but only while the block is at (8,38).
Decisive test for "is the head an obstacle vs is the underlying terrain white": I can't have the block at (38,14) while the head is at (38,20). 
ALTERNATIVE decisive test: check whether the cells at rows 38-42 cols 14-18 are part of the black maze. Evidence: the black region (node 5) — its shape. If the maze's black region includes rows 38-42 cols 13-19, then the red head sits on black cells → the head is an obstacle. If the black region *excludes* rows 38-42 cols 14-18 (i.e., the red head covers white cells), then the terrain there is white (wall) → the corridor is a dead end and the level's
… [36387 caracteres más]

## Paso 7 · nivel 1 · acción 19

**Pensamiento:**

Let me stop theorizing and run a decisive experiment. I'll use a batch and check the head's position after each move.
Experiment: from (8,14): RIGHT×4 → check head; then LEFT×1 → check head; then LEFT×3 → at (8,14); then DOWN×4 → at (32,14); then DOWN (blocked). Total 13 moves. Too long.
Better experiment: I want to know whether the head's position is a function of the block's position (leash) or a lagged replay. Key discriminator: at press 10 the block moved LEFT from (8,38) and the head moved left. Under "lag-4 replay", the head's move at press 10 = replay of the block's move #6... hmm, I need cleaner data.
Actually, here's a much better discriminator that also advances my goal: from the start, do RIGHT×4 (head → 20-24), then DOWN? no.
Hmm, let me think about what experiment could reveal a way past the head. 
IDEA: What if the head can be dragged PAST the corner and UP the vertical part of the path? If the head's route position = f(block's position) = "the nearest point on the path to block+(30,-18)", then no.
NEW IDEA: What if the head's position depends on the block's position, and the head's row CAN change when the block is at a high column and a low row? E.g., the block at (20,38)? Is (20,38) passable? rows 20-24 cols 38-42: col 38 white (rows 19-25 cols 32-38 white) ✗. So no.
What if the block could be at (14,38)? rows 14-18 cols 38-42: col 38 white ✗. No.
So (8,38) is the only high-col position.
Hmm, let me reconsider the "gear" model: head_offset = floor(net_dx/24)*6
… [2263 caracteres más]

```python
g = current_frame.ascii.split('\n')
for r in range(41,57):
    row = g[r][13:56]
    print(r, ''.join('#' if ch=='B' else ('R' if ch=='R' else ('b' if ch=='b' else ('W' if ch=='W' else ch))) for ch in row))
```

```text
41 ##RRRR#######################WWWWWWWWWWWWWW
42 #RRRRR#WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
43 #######WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
44 #######WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
45 #######WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
46 #######WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
47 #######WWWWWWWW
… [451 caracteres más]
```

**Pensamiento:**

Now I see the bottom region clearly. Cols 13-19 are black (the left corridor) down to row 48; row 49 cols 13-42 black; rows 50-54 cols 13-48 black; row 55 cols 13-42 black + the ring.
Wait: row 49: positions 0-28 = cols 13-41 '#'? Let me recount: the string starts at col 13. Row 49: '##############################bbbbbbb#WWWWW' → positions 0-29 = cols 13-42 '#', positions 30-36 = cols 43-49 'b', position 37 = col 50 '#', positions 38-42 = cols 51-55 'W'.
Row 50: '####################################b#WWWWW' → positions 0-35 = cols 13-48 '#', pos 36 = col 49 'b', pos 37 = col 50 '#'.
So rows 50-54: cols 13-48 black ✓ (a wide black area).
Row 55: '##############################bbbbbbb#WWWWW' → cols 13-42 black, cols 43-49 blue, col 50 black.
Row 56: positions 0-28 = cols 13-41 'W' (white!), positions 29-37 = cols 42-50 '#', then white.
So the bottom band: rows 49-55 cols 13-42 black + rows 50-54 cols 43-48 black (the target room). The block's grid row for the bottom band: rows 50-54 ✓ (block at row 50). The block can move right along cols 14,20,...,44 → (50,44) = the target ✓ (and (50,44)'s footprint cols 44-48 ⊂ the room cols 43-48 ✓).
So the route is confirmed: down the left corridor (cols 14-18) → row 49-55 band → right to (50,44).
Hmm OK. And the head blocks at (38,14).
Hmm, let me reconsider: is the head REALLY at rows 38-42? Yes: redinfo shows the blob at rows 38-42 (bbox 36-42 includes the trail's vertical part at rows 36-38 col 40).
Hmm, hold on! Let me reconsider wheth
… [7895 caracteres más]

```python
g = current_frame.ascii.split('\n')
row63 = g[63]
print('bottom bar:', ''.join(sorted(set(row63))), 'b count', row63.count('b'), 'first W at', row63.find('W'), 'w count', row63.count('w'))
print('hud row1:', g[1][0:10], 'row5:', g[5][0:10])
# count total steps used
print('history len', len(history), 'step', current_frame.step)
```

```text
bottom bar: bw b count 55 first W at -1 w count 9
hud row1: WgggWbbbWW row5: WWWWWbbbWW
history len 20 step 19
```

## Paso 7 · nivel 1 · acción 19

**Pensamiento:**

Bottom bar: 55 'b' cells and 9 'w' cells → total 64. So the bar is at 55/64 → maybe 55 steps remaining? Or the bar started at 64 and shrinks 1 per action? At step 19, 55 remain... 64-19 = 45, not 55. Hmm. Maybe the bar shrinks per *move* (not per step), or it started at 64 and shrinks... Let me check the earlier frames' bar length to derive the rate. Actually let me check: history[0].frame row 63 count.
Let me do that plus the HUD check. And then run the decisive experiment.
Actually, the key remaining uncertainty is the head's behavior. Let me design the experiment to maximize information:
Experiment E1 (cost 5): RIGHT, RIGHT, RIGHT, RIGHT (block to (8,38), head→20-24), then check. Then LEFT (block to (8,32)) and check the head. If the head returns to 14-18 → leash confirmed. If the head stays at 20-24 → hysteresis! Then I could push the head right by approaching and then... hmm, but the head only advances when the block *enters* (8,38). With hysteresis, one advance per visit! Then I could shuttle: (8,38) → (8,32) → (8,38) → ... each visit advancing the head 6? But the head is clamped at 20-24 by the formula... unless each visit advances it further.
That's a promising hypothesis! Under the "drag when overlapping" model, the head moves by the block's delta when the block's move starts or ends overlapping red. Visit 1: entering (8,38) → head +6 (→20). Leaving to (8,32) → head -6 (→14). So no net progress. But if the head's movement is clamped at the left end (14), then leaving
… [6586 caracteres más]

```python
seen = {}
for i, h in enumerate(history):
    g = h.frame.ascii.split('\n')
    hud = '|'.join(g[r][0:10] for r in (1,2,3,5))
    seen.setdefault(hud, []).append(i)
for k, v in seen.items():
    print(v[:8], '->', k)
```

```text
[0, 1, 2, 3, 4, 5, 6, 7] -> WbbbWwwwWW|WbWbWwwwWW|WbbbWwwwWW|WbbbWWWWWW
[19] -> WgggWbbbWW|WgWgWbWbWW|WgggWbbbWW|WWWWWbbbWW
```