Ranking at depth 15
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` 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 186
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is occupied by robot1. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 187
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 188
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 189
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is occupied by robot1. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 190
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 191
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is occupied by robot1. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 192
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 194
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is occupied by robot1. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 195
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

### State 196
- `tile_1-1` is painted white. (Goal satisfied)
- `tile_1-2` is clear. (Not painted)
- `tile_1-3` is clear. (Not painted)
- `tile_2-1` is painted black. (Goal satisfied)
- `tile_2-2` is painted white. (Goal satisfied)
- `tile_2-3` is painted black. (Goal satisfied)

**Constraints satisfied: 4**

All states satisfy 4 constraints. Since they are equal in terms of constraints satisfied, they can be ranked equally. However, if we need to rank them, we can consider the action path length or any other heuristic, but based on constraints alone, they are equal.

```ranking
186, 187, 188, 189, 190, 191, 192, 194, 195, 196
```

Final ranking:
Rank 1: State ID 186
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 black. Colors white and black are available for switching.

Rank 2: State ID 187
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 black. Colors white and black are available for switching.

Rank 3: State ID 188
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 4: State ID 189
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 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 5: State ID 190
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 6: State ID 191
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 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 192
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 8: State ID 194
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 black. Colors white and black are available for switching.

Rank 9: State ID 195
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 black. Colors white and black are available for switching.

Rank 10: State ID 196
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.

