Ranking at depth 14
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:

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

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

Let's evaluate each state:

### State 173
- `tile_1-1`: white (satisfied)
- `tile_1-2`: clear (not satisfied)
- `tile_1-3`: clear (not satisfied)
- `tile_2-1`: black (satisfied)
- `tile_2-2`: white (satisfied)
- `tile_2-3`: black (satisfied)

**Constraints satisfied: 4**

### State 176
- `tile_1-1`: white (satisfied)
- `tile_1-2`: clear (not satisfied)
- `tile_1-3`: clear (not satisfied)
- `tile_2-1`: black (satisfied)
- `tile_2-2`: white (satisfied)
- `tile_2-3`: black (satisfied)

**Constraints satisfied: 4**

### State 177
- `tile_1-1`: white (satisfied)
- `tile_1-2`: occupied (not satisfied)
- `tile_1-3`: clear (not satisfied)
- `tile_2-1`: black (satisfied)
- `tile_2-2`: white (satisfied)
- `tile_2-3`: black (satisfied)

**Constraints satisfied: 4**

### State 178
- `tile_1-1`: white (satisfied)
- `tile_1-2`: clear (not satisfied)
- `tile_1-3`: clear (not satisfied)
- `tile_2-1`: black (satisfied)
- `tile_2-2`: white (satisfied)
- `tile_2-3`: black (satisfied)

**Constraints satisfied: 4**

### State 180
- `tile_1-1`: clear (not satisfied)
- `tile_1-2`: clear (not satisfied)
- `tile_1-3`: occupied (not satisfied)
- `tile_2-1`: black (satisfied)
- `tile_2-2`: white (satisfied)
- `tile_2-3`: black (satisfied)

**Constraints satisfied: 3**

### State 183
- `tile_1-1`: clear (not satisfied)
- `tile_1-2`: clear (not satisfied)
- `tile_1-3`: white (satisfied)
- `tile_2-1`: black (satisfied)
- `tile_2-2`: white (satisfied)
- `tile_2-3`: black (satisfied)

**Constraints satisfied: 4**

### State 184
- `tile_1-1`: clear (not satisfied)
- `tile_1-2`: clear (not satisfied)
- `tile_1-3`: occupied (not satisfied)
- `tile_2-1`: black (satisfied)
- `tile_2-2`: white (satisfied)
- `tile_2-3`: black (satisfied)

**Constraints satisfied: 3**

### Ranking
States 173, 176, 177, 178, and 183 each satisfy 4 constraints, while states 180 and 184 satisfy 3 constraints. Therefore, the ranking from best to worst is:

```ranking
173, 176, 177, 178, 183, 180, 184
```

Final ranking:
Rank 1: State ID 173
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 black. Colors white and black are available for switching.

Rank 2: State ID 176
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 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_0-3, holding color white. Colors white and black are available for switching.

Rank 3: State ID 177
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 painted white. 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 178
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 black. Colors white and black are available for switching.

Rank 5: State ID 183
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 painted white. 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 180
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 7: State ID 184
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.

