Ranking at depth 16
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 198
- `tile_1-1` is painted white. (Constraint satisfied)
- `tile_1-2` is clear. (Constraint not satisfied)
- `tile_1-3` is occupied. (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 200
- `tile_1-1` is painted white. (Constraint satisfied)
- `tile_1-2` is clear. (Constraint not satisfied)
- `tile_1-3` is occupied. (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 201
- `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 202
- `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 203
- `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 204
- `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 206
- `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 208
- `tile_1-1` is painted white. (Constraint satisfied)
- `tile_1-2` is occupied. (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 210
- `tile_1-1` is painted white. (Constraint satisfied)
- `tile_1-2` is clear. (Constraint not satisfied)
- `tile_1-3` is occupied. (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**

All states satisfy 4 constraints. Since they are equal, we can rank them in any order. Here is one possible ranking:

```ranking
198, 200, 201, 202, 203, 204, 206, 208, 210
```

Final ranking:
Rank 1: State ID 198
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 black. Colors white and black are available for switching.

Rank 2: State ID 200
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 black. Colors white and black are available for switching.

Rank 3: State ID 201
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 4: State ID 202
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 203
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 6: State ID 204
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 white. Colors white and black are available for switching.

Rank 7: State ID 206
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 8: State ID 208
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 9: State ID 210
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 black. Colors white and black are available for switching.

