Ranking at depth 4
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: 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 15
- **tile_1-1**: clear (not white)
- **tile_1-2**: occupied by robot1 holding black (not painted)
- **tile_1-3**: clear (not white)
- **tile_2-1**: painted black (correct)
- **tile_2-2**: clear (not white)
- **tile_2-3**: clear (not black)

**Constraints satisfied**: 1 (tile_2-1)

### State 18
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: clear (not white)
- **tile_2-1**: clear (not black)
- **tile_2-2**: painted white (correct)
- **tile_2-3**: clear (not black)

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

### State 19
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: occupied by robot1 holding white (not painted)
- **tile_2-1**: clear (not black)
- **tile_2-2**: painted white (correct)
- **tile_2-3**: clear (not black)

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

### State 20
- **tile_1-1**: clear (not white)
- **tile_1-2**: occupied by robot1 holding black (not painted)
- **tile_1-3**: clear (not white)
- **tile_2-1**: clear (not black)
- **tile_2-2**: painted white (correct)
- **tile_2-3**: clear (not black)

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

### State 21
- **tile_1-1**: occupied by robot1 holding white (not painted)
- **tile_1-2**: clear (not black)
- **tile_1-3**: clear (not white)
- **tile_2-1**: clear (not black)
- **tile_2-2**: painted white (correct)
- **tile_2-3**: clear (not black)

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

### State 31
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: occupied by robot1 holding black (not painted)
- **tile_2-1**: clear (not black)
- **tile_2-2**: clear (not white)
- **tile_2-3**: clear (not black)

**Constraints satisfied**: 0

### State 33
- **tile_1-1**: clear (not white)
- **tile_1-2**: clear (not black)
- **tile_1-3**: clear (not white)
- **tile_2-1**: clear (not black)
- **tile_2-2**: painted black (incorrect, should be white)
- **tile_2-3**: clear (not black)

**Constraints satisfied**: 0

### Ranking
Based on the number of constraints satisfied, the ranking is:

```ranking
15, 18, 19, 20, 21, 31, 33
```

States 15, 18, 19, 20, and 21 each satisfy one constraint, but State 15 satisfies a different constraint (tile_2-1) than the others, which might be more strategic depending on the overall goal. States 31 and 33 satisfy no constraints.

Final ranking:
Rank 1: State ID 15
State Description: (tile_0-1: clear, tile_0-2: clear, tile_0-3: clear, tile_1-1: clear, tile_1-2: occupied by robot1 holding color black, tile_1-3: clear, tile_2-1: painted black, tile_2-2: clear, tile_2-3: clear, robot1: on tile_1-2 holding color black, color_white: available, color_black: available)

Rank 2: State ID 18
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 clear. Tile tile_2-2 is painted white. Tile tile_2-3 is clear. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

Rank 3: State ID 19
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 clear. Robot1 is on tile_1-3, holding color white. Colors white and black are available for switching.

Rank 4: State ID 20
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 clear. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

Rank 5: State ID 21
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 clear.Robot1 is on tile_1-1, holding color white.Colors white and black are available for switching.

Rank 6: State ID 31
State Description: (tile_0-1: clear, tile_0-2: clear, tile_0-3: clear, tile_1-1: clear, tile_1-2: clear, tile_1-3: occupied by robot1 holding color black, tile_2-1: clear, tile_2-2: clear, tile_2-3: clear, robot1: on tile_1-3 holding color black, color_white: available, color_black: available)

Rank 7: State ID 33
State Description: (tile_0-1: clear, tile_0-2: clear, tile_0-3: clear, tile_1-1: clear, tile_1-2: clear, tile_1-3: clear, tile_2-1: clear, tile_2-2: painted black, tile_2-3: clear, robot1: on tile_1-2 holding color black, color_white: available, color_black: available)

