Ranking at depth 5
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 34
- `tile_2-1`: painted black (satisfied)
- `tile_1-2`: occupied by robot1 holding color white (not painted, not satisfied)
- Other tiles are clear or occupied, not satisfying any goal constraints.

**Constraints satisfied: 1**

### State 36
- `tile_2-1`: painted black (satisfied)
- `tile_1-3`: occupied by robot1 holding color black (not painted, not satisfied)
- Other tiles are clear or occupied, not satisfying any goal constraints.

**Constraints satisfied: 1**

### State 39
- `tile_2-2`: painted white (satisfied)
- `tile_1-3`: occupied by robot1 holding color black (not painted, not satisfied)
- Other tiles are clear or occupied, not satisfying any goal constraints.

**Constraints satisfied: 1**

### State 40
- `tile_2-1`: painted black (satisfied)
- `tile_2-2`: painted white (satisfied)
- `tile_2-3`: painted black (satisfied)
- `tile_1-2`: occupied by robot1 holding color black (not painted, not satisfied)

**Constraints satisfied: 3**

### State 42
- `tile_2-2`: painted white (satisfied)
- `tile_1-3`: occupied by robot1 holding color black (not painted, not satisfied)
- Other tiles are clear or occupied, not satisfying any goal constraints.

**Constraints satisfied: 1**

### State 43
- `tile_2-2`: painted white (satisfied)
- `tile_2-3`: occupied by robot1 holding color white (not painted, not satisfied)
- Other tiles are clear or occupied, not satisfying any goal constraints.

**Constraints satisfied: 1**

### State 45
- `tile_2-2`: painted white (satisfied)
- `tile_1-3`: occupied by robot1 holding color black (not painted, not satisfied)
- Other tiles are clear or occupied, not satisfying any goal constraints.

**Constraints satisfied: 1**

### State 47
- `tile_2-2`: painted white (satisfied)
- `tile_2-3`: painted black (satisfied)
- `tile_1-2`: occupied by robot1 holding color black (not painted, not satisfied)

**Constraints satisfied: 2**

### Ranking
Based on the number of constraints satisfied, the ranking from best to worst is:

```ranking
40, 47, 34, 36, 39, 42, 43, 45
```

State 40 satisfies the most constraints, followed by State 47. The rest satisfy only one constraint each, so they are ranked equally based on the number of constraints satisfied.

Final ranking:
Rank 1: State ID 40
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 painted black. Robot1 is on tile_1-2, holding color black. Colors white and black are available for switching.

Rank 2: State ID 47
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 black. Colors white and black are available for switching.

Rank 3: State ID 34
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 white, tile_1-3: clear, tile_2-1: painted black, tile_2-2: clear, tile_2-3: clear, robot1: on tile_1-2 holding color white, color_white: available, color_black: available)

Rank 4: State ID 36
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: painted black; Tile_2-2: clear; Tile_2-3: clear. Robot1: on tile_1-3 holding color black. Color_white: available; Color_black: available.

Rank 5: State ID 39
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 black. Colors white and black are available for switching.

Rank 6: State ID 42
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 black. Colors white and black are available for switching.

Rank 7: State ID 43
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 occupied by robot1. Robot1 is on tile_2-3, holding color white. Colors white and black are available for switching.

Rank 8: State ID 45
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 black. Colors white and black are available for switching.

