Ranking at depth 12
Model's reasoning and response:
To rank the states, we need to evaluate how many of the goal constraints are satisfied in each state. The goal constraints are:

1. Row 1:
   - tile_1-1: white
   - tile_1-2: black
   - tile_1-3: white

2. Row 2:
   - tile_2-1: black
   - tile_2-2: white
   - tile_2-3: black

Let's evaluate each state:

### State 144
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: occupied (not white)
- **tile_2-1**: black (correct)
- **tile_2-2**: white (correct)
- **tile_2-3**: black (correct)

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

### State 146
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: occupied (not white)
- **tile_2-1**: black (correct)
- **tile_2-2**: white (correct)
- **tile_2-3**: black (correct)

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

### State 147
- **tile_1-1**: clear (not white)
- **tile_1-2**: occupied (not black)
- **tile_1-3**: clear (not white)
- **tile_2-1**: black (correct)
- **tile_2-2**: white (correct)
- **tile_2-3**: black (correct)

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

### State 149
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: occupied (not white)
- **tile_2-1**: black (correct)
- **tile_2-2**: white (correct)
- **tile_2-3**: black (correct)

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

### State 153
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: clear (not white)
- **tile_2-1**: black (correct)
- **tile_2-2**: white (correct)
- **tile_2-3**: black (correct)

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

### State 154
- **tile_1-1**: occupied (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: clear (not white)
- **tile_2-1**: black (correct)
- **tile_2-2**: white (correct)
- **tile_2-3**: black (correct)

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

### State 155
- **tile_1-1**: white (correct)
- **tile_1-2**: clear (not black)
- **tile_1-3**: clear (not white)
- **tile_2-1**: black (correct)
- **tile_2-2**: white (correct)
- **tile_2-3**: black (correct)

**Constraints satisfied**: 4 (tile_1-1, tile_2-1, tile_2-2, tile_2-3)

### Ranking
State 155 satisfies the most constraints, followed by the others which satisfy the same number of constraints. Therefore, the ranking is:

```ranking
155, 144, 146, 147, 149, 153, 154
```

Final ranking:
Rank 1: State ID 155
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 painted white. 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 2: State ID 144
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 white. Colors white and black are available for switching.

Rank 3: State ID 146
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 white. Colors white and black are available for switching.

Rank 4: State ID 147
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 5: State ID 149
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 white. Colors white and black are available for switching.

Rank 6: State ID 153
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 white. Colors white and black are available for switching.

Rank 7: State ID 154
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.

