Ranking at depth 11
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 129
- `tile_1-1`: Clear (not painted white)
- `tile_1-2`: Occupied (not painted black)
- `tile_1-3`: Clear (not painted white)
- `tile_2-1`: Painted black (correct)
- `tile_2-2`: Painted white (correct)
- `tile_2-3`: Painted black (correct)

**Constraints satisfied:** 3 (tiles `tile_2-1`, `tile_2-2`, `tile_2-3`)

### State 133
- `tile_1-1`: Clear (not painted white)
- `tile_1-2`: Clear (not painted black)
- `tile_1-3`: Occupied (not painted white)
- `tile_2-1`: Painted black (correct)
- `tile_2-2`: Painted white (correct)
- `tile_2-3`: Painted black (correct)

**Constraints satisfied:** 3 (tiles `tile_2-1`, `tile_2-2`, `tile_2-3`)

### State 135
- `tile_1-1`: Clear (not painted white)
- `tile_1-2`: Occupied (not painted black)
- `tile_1-3`: Clear (not painted white)
- `tile_2-1`: Painted black (correct)
- `tile_2-2`: Painted white (correct)
- `tile_2-3`: Painted black (correct)

**Constraints satisfied:** 3 (tiles `tile_2-1`, `tile_2-2`, `tile_2-3`)

### State 136
- `tile_1-1`: Clear (not painted white)
- `tile_1-2`: Clear (not painted black)
- `tile_1-3`: Clear (not painted white)
- `tile_2-1`: Painted black (correct)
- `tile_2-2`: Painted white (correct)
- `tile_2-3`: Painted black (correct)

**Constraints satisfied:** 3 (tiles `tile_2-1`, `tile_2-2`, `tile_2-3`)

### State 137
- `tile_1-1`: Occupied (not painted white)
- `tile_1-2`: Clear (not painted black)
- `tile_1-3`: Clear (not painted white)
- `tile_2-1`: Painted black (correct)
- `tile_2-2`: Painted white (correct)
- `tile_2-3`: Painted black (correct)

**Constraints satisfied:** 3 (tiles `tile_2-1`, `tile_2-2`, `tile_2-3`)

### State 138
- `tile_1-1`: Clear (not painted white)
- `tile_1-2`: Occupied (not painted black)
- `tile_1-3`: Clear (not painted white)
- `tile_2-1`: Painted black (correct)
- `tile_2-2`: Painted white (correct)
- `tile_2-3`: Painted black (correct)

**Constraints satisfied:** 3 (tiles `tile_2-1`, `tile_2-2`, `tile_2-3`)

### State 140
- `tile_1-1`: Clear (not painted white)
- `tile_1-2`: Occupied (not painted black)
- `tile_1-3`: Clear (not painted white)
- `tile_2-1`: Painted black (correct)
- `tile_2-2`: Painted white (correct)
- `tile_2-3`: Painted black (correct)

**Constraints satisfied:** 3 (tiles `tile_2-1`, `tile_2-2`, `tile_2-3`)

All states satisfy the same number of constraints (3), so they are equally ranked. However, if we consider the robot's position and color, we might prioritize states where the robot is closer to achieving the next goal constraint. Since all states are equal in terms of constraints satisfied, we can rank them arbitrarily.

```ranking
129, 133, 135, 136, 137, 138, 140
```

Final ranking:
Rank 1: State ID 129
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 white. Colors white and black are available for switching.

Rank 2: State ID 133
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 painted black. 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 135
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 white. Colors white and black are available for switching.

Rank 4: State ID 136
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 white. Colors white and black are available for switching.

Rank 5: State ID 137
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 black. Colors white and black are available for switching.

Rank 6: State ID 138
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is occupied by robot1. 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_0-2, holding color black. Colors white and black are available for switching.

Rank 7: State ID 140
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 white. Colors white and black are available for switching.

