Ranking at depth 16
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. Preference for states where the tile directly above the robot is not painted, unless all tiles in the row above are painted, in which case the robot should move down.
3. States with incorrectly colored tiles are ranked last.

Let's evaluate each state:

- **State 87**: 
  - Tiles painted correctly: 3 (tile_0-0, tile_0-1, tile_0-3).
  - Tile directly above the robot (tile_0-4) is not painted.
  - Robot is on tile_1-4, which is correct since not all tiles in row 0 are painted.
  
- **State 89**: 
  - Tiles painted correctly: 3 (tile_0-0, tile_0-1, tile_0-3).
  - Tile directly above the robot (tile_0-4) is not painted.
  - Robot is on tile_1-4, which is correct since not all tiles in row 0 are painted.

- **State 90**: 
  - Tiles painted correctly: 4 (tile_0-0, tile_0-1, tile_0-3, tile_0-4).
  - Tile directly above the robot (tile_0-4) is painted correctly.
  - Robot is on tile_1-4, which is correct since not all tiles in row 0 are painted.

- **State 91**: 
  - Tiles painted correctly: 3 (tile_0-0, tile_0-1, tile_0-3).
  - Tile directly above the robot (tile_0-4) is not painted.
  - Robot is on tile_1-4, which is correct since not all tiles in row 0 are painted.

- **State 92**: 
  - Tiles painted correctly: 3 (tile_0-0, tile_0-1, tile_0-3).
  - Tile directly above the robot (tile_0-4) is not painted.
  - Robot is on tile_1-4, which is correct since not all tiles in row 0 are painted.

**Ranking Explanation:**

- **State 90** is the best because it has the most tiles correctly painted (4 tiles).
- **States 87, 89, 91, and 92** all have 3 tiles correctly painted. Since the tile directly above the robot is not painted in these states, they are equally ranked. However, since they are all in the same position and have the same number of correctly painted tiles, they can be considered equivalent.

```ranking
90, 87, 89, 91, 92
```

Final ranking:
Rank 1: State ID 90
State Description: Robot1, standing on tile_1-4, paints the tile above it, tile_0-4, with black paint. Tile_0-4 is now painted black and is no longer clear.

Rank 2: State ID 87
State Description: Robot1 moves from tile_1-3 to tile_1-4, now occupying tile_1-4 and leaving tile_1-3 clear.

Rank 3: State ID 89
State Description: Robot1, located on tile_1-4, changes its paint gun color from black to white. The robot is now holding white paint.

Rank 4: State ID 91
State Description: Robot1 is on tile_1-4, holding white paint. Tile_1-4 is occupied by Robot1, and tile_1-3 is clear.

Rank 5: State ID 92
State Description: Robot1 is on tile_1-4 and has changed its paint gun color from white to black.

