Ranking at depth 10
Model's reasoning and response:
To rank the states, we need to evaluate how close each state is to the goal state, which requires the first row of tiles to be painted in an alternating color pattern starting with black. The criteria for ranking are:

1. Number of tiles correctly colored according to the goal state.
2. Tiles directly above the robots should not be painted if they are not supposed to be.
3. If all tiles in the row above are painted, the robot should move down.

Let's evaluate each state:

- **State 45**: 
  - Tiles painted: tile_0-1 (black), tile_0-2 (black), tile_0-3 (black).
  - Incorrectly painted: tile_0-3 should be white.
  - Robot is on tile_1-4, holding black paint.
  - Ranking: Incorrectly painted tile, so it ranks lower.

- **State 46**: 
  - Tiles painted: tile_0-1 (black), tile_0-2 (black), tile_0-3 (black).
  - Incorrectly painted: tile_0-3 should be white.
  - Robot is on tile_1-2, holding black paint.
  - Ranking: Incorrectly painted tile, so it ranks lower.

- **State 47**: 
  - Tiles painted: tile_0-1 (black), tile_0-2 (black), tile_0-3 (white).
  - Correctly painted: tile_0-3 is now correct.
  - Robot is on tile_1-3, holding white paint.
  - Ranking: Correctly painted tiles, ranks higher.

- **State 48**: 
  - Tiles painted: tile_0-1 (black), tile_0-2 (black), tile_0-3 (white).
  - Correctly painted: tile_0-3 is correct.
  - Robot is on tile_1-4, holding white paint.
  - Ranking: Correctly painted tiles, ranks higher.

- **State 49**: 
  - Tiles painted: tile_0-0 (black), tile_0-1 (white).
  - Correctly painted: tile_0-0 and tile_0-1 are correct.
  - Robot is on tile_1-2, holding white paint.
  - Ranking: More tiles correctly painted, ranks highest.

- **State 50**: 
  - Tiles painted: tile_0-0 (black), tile_0-1 (white).
  - Correctly painted: tile_0-0 and tile_0-1 are correct.
  - Robot is on tile_1-2, holding white paint.
  - Ranking: Same as State 49, ranks highest.

- **State 51**: 
  - Tiles painted: tile_0-0 (black), tile_0-1 (white).
  - Correctly painted: tile_0-0 and tile_0-1 are correct.
  - Robot is on tile_1-1, holding black paint.
  - Ranking: Same as State 49 and 50, ranks highest.

Final ranking based on the criteria:

```ranking
49, 50, 51, 47, 48, 45, 46
```

Final ranking:
Rank 1: State ID 49
State Description: Robot1 moves from tile_1-1 to tile_1-2. Tile_1-1 is now clear, and tile_1-2 is occupied by Robot1, which is holding the white paint gun.

Rank 2: State ID 50
State Description: Robot1 moves from tile_1-1 to tile_1-2, holding the white paint gun. Tile_1-1 is now clear, and tile_1-2 is occupied by Robot1.

Rank 3: State ID 51
State Description: Robot1, standing on tile_1-1, has changed its paint gun color from white to black.

Rank 4: State ID 47
State Description: Tile_0-3 is now painted white. Robot1 remains on tile_1-3, holding white paint.

Rank 5: State ID 48
State Description: Robot1 moves from tile_1-3 to tile_1-4. Tile_1-3 becomes clear, and tile_1-4 is now occupied by Robot1, which is holding white paint.

Rank 6: State ID 45
State Description: Robot1 moves from tile_1-3 to tile_1-4. Tile_1-3 becomes clear, and tile_1-4 is now occupied by Robot1, which is holding black paint.

Rank 7: State ID 46
State Description: Robot1 moves from tile_1-3 to tile_1-2. Tile_1-3 becomes clear, and tile_1-2 is now occupied by Robot1, which is holding black paint.

