Ranking at depth 8
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 78
- `tile_1-1`: Occupied, 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 (tiles `tile_2-2` and `tile_2-3`).

### State 79
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Clear, not painted.
- `tile_1-3`: Occupied, not painted.
- `tile_2-1`: Clear, not painted.
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

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

### State 81
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Occupied, 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 (tiles `tile_2-2` and `tile_2-3`).

### State 87
- `tile_1-1`: Occupied, 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 (tiles `tile_2-2` and `tile_2-3`).

### State 89
- `tile_1-1`: Clear, not painted.
- `tile_1-2`: Clear, not painted.
- `tile_1-3`: Clear, not painted.
- `tile_2-1`: Occupied, not painted.
- `tile_2-2`: Painted white (correct).
- `tile_2-3`: Painted black (correct).

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

### State 90
- `tile_1-1`: Occupied, 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 (tiles `tile_2-2` and `tile_2-3`).

All states satisfy the same number of constraints (2). Therefore, they are equally ranked based on the number of constraints satisfied. Since no state is closer to satisfying additional constraints, the ranking is arbitrary among them.

```ranking
78, 79, 81, 87, 89, 90
```

Final ranking:
Rank 1: State ID 78
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 2: State ID 79
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.

Rank 3: State ID 81
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 clear. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_1-2, holding color white. Colors white and black are available for switching.

Rank 4: State ID 87
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 holding color black. 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 5: State ID 89
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 occupied by robot1 holding color white. Tile tile_2-2 is painted white. Tile tile_2-3 is painted black. Robot1 is on tile_2-1, holding color white. Colors white and black are available for switching.

Rank 6: State ID 90
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 holding color black. 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.

