Ranking at depth 6
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 49
- tile_1-1: clear (not white)
- tile_1-2: clear (not black)
- tile_1-3: occupied (not white)
- tile_2-1: clear (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied:** 2 (tile_2-2, tile_2-3)

### State 50
- tile_1-1: occupied (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: clear (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied:** 2 (tile_2-2, tile_2-3)

### State 53
- tile_1-1: occupied (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: clear (not black)
- tile_2-2: white (correct)
- tile_2-3: black (correct)

**Constraints satisfied:** 2 (tile_2-2, tile_2-3)

### State 58
- tile_1-1: clear (not white)
- tile_1-2: occupied (not black)
- tile_1-3: clear (not white)
- tile_2-1: black (correct)
- tile_2-2: white (correct)
- tile_2-3: clear (not black)

**Constraints satisfied:** 2 (tile_2-1, tile_2-2)

### State 59
- tile_1-1: clear (not white)
- tile_1-2: clear (not black)
- tile_1-3: occupied (not white)
- tile_2-1: black (correct)
- tile_2-2: clear (not white)
- tile_2-3: clear (not black)

**Constraints satisfied:** 1 (tile_2-1)

### State 60
- tile_1-1: clear (not white)
- tile_1-2: clear (not black)
- tile_1-3: clear (not white)
- tile_2-1: black (correct)
- tile_2-2: clear (not white)
- tile_2-3: black (correct)

**Constraints satisfied:** 2 (tile_2-1, tile_2-3)

### State 62
- tile_1-1: clear (not white)
- tile_1-2: occupied (not black)
- tile_1-3: clear (not white)
- tile_2-1: black (correct)
- tile_2-2: clear (not white)
- tile_2-3: clear (not black)

**Constraints satisfied:** 1 (tile_2-1)

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

```ranking
49, 50, 53, 58, 60, 59, 62
```

States 49, 50, and 53 satisfy the same number of constraints, but they are ranked first as they satisfy the constraints for tiles that are more challenging to reach (row 2). State 58 and 60 also satisfy two constraints but are ranked lower due to the specific tiles they satisfy. States 59 and 62 satisfy only one constraint each.

Final ranking:
Rank 1: State ID 49
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 painted black. Robot1 is on tile_1-3, holding color black. Colors white and black are available for switching.

Rank 2: State ID 50
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 occupied by robot1 holding color black. 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_1-1, holding color black. Colors white and black are available for switching.

Rank 3: State ID 53
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 occupied by robot1 holding color black. 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_1-1, holding color black. Colors white and black are available for switching.

Rank 4: State ID 58
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: clear, tile_2-1: painted black, tile_2-2: painted white, tile_2-3: clear, robot1: on tile_1-2 holding color white, color_white: available, color_black: available)

Rank 5: State ID 60
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: clear; Tile_2-1: painted black; Tile_2-2: clear; Tile_2-3: painted black. Robot1: on tile_1-3 holding color black. Color_white: available; Color_black: available.

Rank 6: State ID 59
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 white- tile_2-1: painted black- tile_2-2: clear- tile_2-3: clear- robot1: on tile_1-3 holding color white- color_white: available- color_black: available

Rank 7: State ID 62
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 black; Tile_1-3: clear; Tile_2-1: painted black; Tile_2-2: clear; Tile_2-3: clear. Robot1: on tile_1-2 holding color black. Color_white: available; Color_black: available.

