Ranking at depth 10
Model's reasoning and response:
To solve this problem, we need to compare each state against the goal state and determine how many constraints are satisfied. The goal state constraints are:

1. Block 'c' is on the table.
2. Block 'a' is on block 'c'.
3. Block 'b' is on block 'a'.
4. Block 'd' is on block 'b'.

Let's evaluate each state:

### State 54
- **Block 'c' is on the table:** Yes
- **Block 'a' is on block 'c':** Yes
- **Block 'b' is on block 'a':** Yes
- **Block 'd' is on block 'b':** Yes

**Constraints satisfied:** 4

### State 55
- **Block 'c' is on the table:** Yes
- **Block 'a' is on block 'c':** Yes
- **Block 'b' is on block 'a':** Yes
- **Block 'd' is on block 'b':** Yes

**Constraints satisfied:** 4

### State 56
- **Block 'c' is on the table:** No
- **Block 'a' is on block 'c':** No
- **Block 'b' is on block 'a':** No
- **Block 'd' is on block 'b':** Yes

**Constraints satisfied:** 1

### State 57
- **Block 'c' is on the table:** Yes
- **Block 'a' is on block 'c':** Yes
- **Block 'b' is on block 'a':** No
- **Block 'd' is on block 'b':** Yes

**Constraints satisfied:** 3

### State 59
- **Block 'c' is on the table:** Yes
- **Block 'a' is on block 'c':** Yes
- **Block 'b' is on block 'a':** Yes
- **Block 'd' is on block 'b':** No

**Constraints satisfied:** 3

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

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

- States 54 and 55 satisfy all 4 constraints.
- States 57 and 59 satisfy 3 constraints.
- State 56 satisfies 1 constraint.

Final ranking:
Rank 1: State ID 54
State Description: The hand is now empty. Block 'd' is on block 'b' and is clear. Block 'b' is not clear and is on block 'a'. Block 'a' is not clear and is on block 'c'. Block 'c' is on the table and not clear.

Rank 2: State ID 55
State Description: The hand is now empty. Block 'd' is on block 'b' and is clear. Block 'b' is not clear. Block 'a' is not clear. Block 'c' remains under block 'a' and is not clear. The diagram now shows block 'd' on top of block 'b', completing the stack.

Rank 3: State ID 57
State Description: The hand is now empty. Block 'd' is on block 'b', and block 'b' is no longer clear. Block 'a' is on block 'c', and block 'c' is on the table. The diagram will show block 'd' on top of block 'b', with the hand empty.

Rank 4: State ID 59
State Description: The hand is now empty. Block 'b' is on block 'a', and block 'a' is on block 'c'. Block 'd' remains on the table and clear. The diagram would show block 'b' stacked on block 'a', forming a tower with 'c' at the base.

Rank 5: State ID 56
State Description: The hand is now empty. Block 'a' is on block 'c', and block 'c' is supporting block 'a' and is no longer clear. Block 'b' is supporting block 'd' and is not clear. Block 'd' is on block 'b' and is clear.

