Ranking at depth 13
Model's reasoning and response:
To solve this problem, we need to evaluate each state based on how many goal constraints are satisfied. 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 156
- `tile_1-1` is painted white. (Constraint satisfied)
- `tile_1-2` is clear. (Constraint not satisfied)
- `tile_1-3` is clear. (Constraint not satisfied)
- `tile_2-1` is painted black. (Constraint satisfied)
- `tile_2-2` is painted white. (Constraint satisfied)
- `tile_2-3` is painted black. (Constraint satisfied)

**Constraints satisfied: 4**

### State 157
- `tile_1-1` is painted white. (Constraint satisfied)
- `tile_1-2` is clear. (Constraint not satisfied)
- `tile_1-3` is clear. (Constraint not satisfied)
- `tile_2-1` is painted black. (Constraint satisfied)
- `tile_2-2` is painted white. (Constraint satisfied)
- `tile_2-3` is painted black. (Constraint satisfied)

**Constraints satisfied: 4**

### State 160
- `tile_1-1` is clear. (Constraint not satisfied)
- `tile_1-2` is occupied by robot1. (Constraint not satisfied)
- `tile_1-3` is clear. (Constraint not satisfied)
- `tile_2-1` is painted black. (Constraint satisfied)
- `tile_2-2` is painted white. (Constraint satisfied)
- `tile_2-3` is painted black. (Constraint satisfied)

**Constraints satisfied: 3**

### State 161
- `tile_1-1` is clear. (Constraint not satisfied)
- `tile_1-2` is clear. (Constraint not satisfied)
- `tile_1-3` is clear. (Constraint not satisfied)
- `tile_2-1` is painted black. (Constraint satisfied)
- `tile_2-2` is painted white. (Constraint satisfied)
- `tile_2-3` is painted black. (Constraint satisfied)

**Constraints satisfied: 3**

### State 164
- `tile_1-1` is clear. (Constraint not satisfied)
- `tile_1-2` is clear. (Constraint not satisfied)
- `tile_1-3` is clear. (Constraint not satisfied)
- `tile_2-1` is painted black. (Constraint satisfied)
- `tile_2-2` is painted white. (Constraint satisfied)
- `tile_2-3` is painted black. (Constraint satisfied)

**Constraints satisfied: 3**

### State 165
- `tile_1-1` is clear. (Constraint not satisfied)
- `tile_1-2` is occupied by robot1. (Constraint not satisfied)
- `tile_1-3` is clear. (Constraint not satisfied)
- `tile_2-1` is painted black. (Constraint satisfied)
- `tile_2-2` is painted white. (Constraint satisfied)
- `tile_2-3` is painted black. (Constraint satisfied)

**Constraints satisfied: 3**

### State 170
- `tile_1-1` is clear. (Constraint not satisfied)
- `tile_1-2` is occupied by robot1. (Constraint not satisfied)
- `tile_1-3` is clear. (Constraint not satisfied)
- `tile_2-1` is painted black. (Constraint satisfied)
- `tile_2-2` is painted white. (Constraint satisfied)
- `tile_2-3` is painted black. (Constraint satisfied)

**Constraints satisfied: 3**

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

```ranking
156, 157, 160, 161, 164, 165, 170
```

Final ranking:
Rank 1: State ID 156
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 black. Colors white and black are available for switching.

Rank 2: State ID 157
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 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_0-2, holding color white. Colors white and black are available for switching.

Rank 3: State ID 160
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 161
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is occupied by robot1. 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_0-3, holding color white. Colors white and black are available for switching.

Rank 5: State ID 164
State Description: Tile tile_0-1 is clear. Tile tile_0-2 is clear. Tile tile_0-3 is occupied by robot1. 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_0-3, holding color white. Colors white and black are available for switching.

Rank 6: State ID 165
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 7: State ID 170
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.

