Ranking at depth 7
Model's reasoning and response:
To solve this problem, we need to evaluate each state based on how many of the goal constraints are satisfied. The goal is to clear the top three rows (rows 0, 1, and 2) of the grid. Specifically, the positions that must be clear are:

- **Row 2:** f2-0f, f2-1f, f2-2f, f2-3f
- **Row 1:** f1-0f, f1-1f, f1-2f, f1-3f
- **Row 0:** f0-0f, f0-1f, f0-2f, f0-3f

Let's evaluate each state:

### State 54
- **Clear Positions:**
  - Row 2: f2-1f, f2-2f, f2-3f
  - Row 1: f1-0f, f1-1f, f1-2f, f1-3f
  - Row 0: f0-0f, f0-1f, f0-2f, f0-3f
- **Constraints Satisfied:** 7 (all of row 0 and row 1, and three positions in row 2)

### State 55
- **Clear Positions:**
  - Row 2: f2-0f, f2-2f, f2-3f
  - Row 1: f1-0f, f1-1f, f1-2f, f1-3f
  - Row 0: f0-0f, f0-1f, f0-2f, f0-3f
- **Constraints Satisfied:** 7 (all of row 0 and row 1, and three positions in row 2)

### State 56
- **Clear Positions:**
  - Row 2: f2-1f, f2-2f, f2-3f
  - Row 1: f1-0f, f1-1f, f1-2f, f1-3f
  - Row 0: f0-0f, f0-1f, f0-2f, f0-3f
- **Constraints Satisfied:** 7 (all of row 0 and row 1, and three positions in row 2)

### State 57
- **Clear Positions:**
  - Row 2: f2-0f, f2-1f, f2-2f, f2-3f
  - Row 1: f1-0f, f1-1f, f1-2f, f1-3f
  - Row 0: f0-0f, f0-1f, f0-2f, f0-3f
- **Constraints Satisfied:** 8 (all of row 0, row 1, and row 2)

### State 59
- **Clear Positions:**
  - Row 2: f2-0f, f2-3f
  - Row 1: f1-0f, f1-2f, f1-3f
  - Row 0: f0-0f, f0-1f, f0-2f, f0-3f
- **Constraints Satisfied:** 7 (all of row 0 and row 1, and two positions in row 2)

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

```ranking
57, 54, 55, 56, 59
```

- **State 57** satisfies all 8 constraints.
- **States 54, 55, and 56** each satisfy 7 constraints, but they are equivalent in terms of goal satisfaction.
- **State 59** satisfies 7 constraints but has fewer clear positions in row 2 compared to the others.

Final ranking:
Rank 1: State ID 57
State Description: - **rightl0 (L-shaped piece)**: Occupies positions f4-1f, f5-1f, and f5-2f; color is blue.- **rightl1 (L-shaped piece)**: Occupies positions f2-2f, f3-2f, and f3-3f; color is green.- **square0 (One-square piece)**: Moved to position f3-1f; color is red.- **square1 (One-square piece)**: Remains in position f3-0f; color is yellow.- **Grid Cells (Unoccupied)**: Clear positions are now f0-0f, f0-1f, f0-2f, f0-3f, f1-0f, f1-1f, f1-2f, f1-3f, f2-0f, f2-1f, f4-0f, f4-3f, f5-0f, f5-3f.

Rank 2: State ID 54
State Description: - **rightl0 (L-shaped piece)**: Occupies positions f4-1f, f5-1f, and f5-2f; color is blue.- **rightl1 (L-shaped piece)**: Occupies positions f3-2f, f4-2f, and f4-3f; color is green.- **square0 (One-square piece)**: Now occupies position f2-0f; color is red.- **square1 (One-square piece)**: Remains in position f3-0f; color is yellow.- **Grid Cells (Unoccupied)**: Clear positions are now f0-0f, f0-1f, f0-2f, f0-3f, f1-0f, f1-1f, f1-2f, f1-3f, f2-1f, f2-2f, f2-3f, f3-1f, f3-3f, f4-0f, f5-0f, f5-3f.

Rank 3: State ID 55
State Description: - **rightl0 (L-shaped piece)**: Occupies positions f4-1f, f5-1f, and f5-2f; color is blue.- **rightl1 (L-shaped piece)**: Occupies positions f3-2f, f4-2f, and f4-3f; color is green.- **square0 (One-square piece)**: Now occupies position f2-1f; color is red.- **square1 (One-square piece)**: Remains in position f3-0f; color is yellow.- **Grid Cells (Unoccupied)**: Clear positions are now f0-0f, f0-1f, f0-2f, f0-3f, f1-0f, f1-1f, f1-2f, f1-3f, f2-0f, f2-2f, f2-3f, f3-1f, f3-3f, f4-0f, f5-0f, f5-3f.

Rank 4: State ID 56
State Description: - **rightl0 (L-shaped piece)**: Occupies positions f4-1f, f5-1f, and f5-2f; color is blue.- **rightl1 (L-shaped piece)**: Moved to positions f3-2f, f4-2f, and f4-3f; color is green.- **square0 (One-square piece)**: Remains in position f2-0f; color is red.- **square1 (One-square piece)**: Remains in position f3-0f; color is yellow.- **Grid Cells (Unoccupied)**: Clear positions are now f0-0f, f0-1f, f0-2f, f0-3f, f1-0f, f1-1f, f1-2f, f1-3f, f2-1f, f2-2f, f2-3f, f3-1f, f4-0f, f5-0f, f5-3f.

Rank 5: State ID 59
State Description: - **rightl0 (L-shaped piece)**: Occupies positions f4-1f, f5-1f, and f5-2f; color is blue.- **rightl1 (L-shaped piece)**: Occupies positions f1-1f, f2-1f, and f2-2f; color is green.- **square0 (One-square piece)**: Now occupies position f3-2f; color is red.- **square1 (One-square piece)**: Occupies position f3-0f; color is yellow.- **Grid Cells (Unoccupied)**: Clear positions are f0-0f, f0-1f, f0-2f, f0-3f, f1-0f, f1-2f, f1-3f, f2-0f, f2-3f, f3-1f, f3-3f, f4-0f, f4-3f, f5-0f, f5-3f.

