Ranking at depth 10
Model's reasoning and response:
To rank the states, we need to evaluate how many goal constraints each state satisfies. The goal constraints are:

1. **Row 1:**
   - `tile_1-1` should be painted white.
   - `tile_1-2` should be painted black.
   - `tile_1-3` should be painted white.

2. **Row 2:**
   - `tile_2-1` should be painted black.
   - `tile_2-2` should be painted white.
   - `tile_2-3` should be painted black.

Let's evaluate each state:

### State 113
- `tile_1-1`: Occupied by robot1, not painted.
- `tile_1-2`: Clear, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Painted black (correct).
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 3 (all tiles in Row 2).

### State 114
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Occupied by robot1, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Painted black (correct).
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 3 (all tiles in Row 2).

### State 115
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Clear, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Painted black (correct).
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 3 (all tiles in Row 2).

### State 116
- `tile_1-1`: Occupied by robot1, not painted.
- `tile_1-2`: Clear, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Painted black (correct).
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 3 (all tiles in Row 2).

### State 117
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Occupied by robot1, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Painted black (correct).
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 3 (all tiles in Row 2).

### State 124
- `tile_1-1`: Occupied by robot1, not painted.
- `tile_1-2`: Clear, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Clear, not painted.
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 2 (`tile_2-2` and `tile_2-3`).

### State 125
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Clear, not painted.
- `tile_1-3`: Occupied by robot1, not painted.
- `tile_2-1`: Clear, not painted.
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 2 (`tile_2-2` and `tile_2-3`).

### State 126
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Occupied by robot1, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Painted black (correct).
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

**Constraints satisfied:** 3 (all tiles in Row 2).

### Ranking
All states except 124 and 125 satisfy 3 constraints, while 124 and 125 satisfy 2 constraints. Therefore, the ranking from best to worst is:

```ranking
113, 114, 115, 116, 117, 126, 124, 125
```

Final ranking:
Rank 1: State ID 113
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is occupied by robot1. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-1, holding color white. Colors white and black are available for switching.

Rank 2: State ID 114
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is occupied by robot1. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

Rank 3: State ID 115
State Description: Tile tile_0-1 is occupied by robot1. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_0-1, holding color black. Colors white and black are available for switching.

Rank 4: State ID 116
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-1, holding color white. Colors white and black are available for switching.

Rank 5: State ID 117
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is occupied by robot1. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

Rank 6: State ID 126
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is occupied by robot1. Tile tile_1-3 is clear. Tile tile_2-1 is painted black. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

Rank 7: State ID 124
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is occupied by robot1. Tile tile_1-2 is clear. Tile tile_1-3 is clear. Tile tile_2-1 is clear. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-1, holding color black. Colors white and black are available for switching.

Rank 8: State ID 125
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is clear. Tile tile_1-1 is clear. Tile tile_1-2 is clear. Tile tile_1-3 is occupied by robot1. Tile tile_2-1 is clear. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-3, holding color black. Colors white and black are available for switching.

