Ranking at depth 3
Model's reasoning and response:
To solve this problem, we need to evaluate each state against the goal constraints and rank them based on how many constraints are satisfied. The goal constraints are:

1. Shot1 must contain cocktail1, which is the cocktail created by mixing ingredient1 and ingredient2.
2. Shot2 must contain cocktail2, which is the cocktail created by mixing ingredient1 and ingredient2.

Let's evaluate each state:

### State 8
- **Shot1**: Empty and held by the left hand.
- **Shot2**: Clean and empty on the table.
- **Shaker1**: Contains ingredient1, used, unshaken.

**Constraints Satisfied**: None. Shot1 and Shot2 do not contain the required cocktails.

### State 9
- **Shot1**: Held by the left hand, contains ingredient1, used.
- **Shot2**: Held by the right hand, clean, and empty.
- **Shaker1**: Clean, empty.

**Constraints Satisfied**: None. Shot1 contains only ingredient1, not the cocktail. Shot2 is empty.

### State 10
- **Shot1**: On the table, contains ingredient1, used.
- **Shot2**: Clean and empty on the table.
- **Shaker1**: Clean, empty.

**Constraints Satisfied**: None. Shot1 contains only ingredient1, not the cocktail. Shot2 is empty.

### State 11
- **Shot1**: Held by the left hand, now empty, and not clean.
- **Shot2**: Clean and empty on the table.
- **Shaker1**: Contains ingredient2, not clean, unshaken.

**Constraints Satisfied**: None. Shot1 is empty. Shot2 is empty.

### State 12
- **Shot1**: Clean, contains ingredient2, on the table.
- **Shot2**: Clean and empty on the table.
- **Shaker1**: Clean, empty.

**Constraints Satisfied**: None. Shot1 contains only ingredient2, not the cocktail. Shot2 is empty.

### State 13
- **Shot1**: Held by left hand, clean, empty.
- **Shot2**: Clean, empty, on the table.
- **Shaker1**: Clean, empty.

**Constraints Satisfied**: None. Both shots are empty.

### State 15
- **Shot1**: Clean, empty, on the table.
- **Shot3**: Clean, empty, held by right hand.
- **Shaker1**: Contains ingredient1, not clean.

**Constraints Satisfied**: None. Both shots are empty.

### State 16
- **Shot1**: Clean, empty, held by right hand.
- **Shot2**: Clean, empty, on the table.
- **Shaker1**: Contains ingredient1, not clean.

**Constraints Satisfied**: None. Both shots are empty.

Since no state satisfies any of the goal constraints, we need to evaluate how close each state is to satisfying a constraint. The closest states are those where the shaker contains both ingredients and is unshaken, ready to create a cocktail.

### Ranking
- **State 8**: Shaker1 contains ingredient1, ready to add ingredient2.
- **State 11**: Shaker1 contains ingredient2, ready to add ingredient1.
- **State 9**: Shot1 contains ingredient1, but no shaker progress.
- **State 10**: Shot1 contains ingredient1, but no shaker progress.
- **State 12**: Shot1 contains ingredient2, but no shaker progress.
- **State 15**: Shaker1 contains ingredient1, but no progress on mixing.
- **State 16**: Shaker1 contains ingredient1, but no progress on mixing.
- **State 13**: No progress on any constraint.

```ranking
8, 11, 9, 10, 12, 15, 16, 13
```

Final ranking:
Rank 1: State ID 8
State Description: - Shot1 is empty and held by the left hand.- Shot2 is clean and empty on the table.- Shot3 is clean and empty on the table.- Shaker1 contains ingredient1, is used, unshaken, and at fill level l1 on the table.- Dispenser1 contains ingredient1 (color: red).- Dispenser2 contains ingredient2 (color: blue).- Left hand is holding empty shot1.- Right hand is empty.

Rank 2: State ID 11
State Description: - Shot1 is held by the left hand, now empty, and not clean.- Shot2 is clean and empty on the table.- Shot3 is clean and empty on the table.- Shaker1 is on the table, contains ingredient2, not clean, at fill level l1, and unshaken.- Dispenser1 contains ingredient1 (color: red).- Dispenser2 contains ingredient2 (color: blue).- Left hand is holding shot1, now empty.- Right hand is empty.

Rank 3: State ID 9
State Description: - Shot1 is held by the left hand, contains ingredient1, and is used.- Shot2 is held by the right hand, is clean, and empty.- Shot3 is clean and empty on the table.- Shaker1 is clean, empty, and at fill level l0 on the table.- Dispenser1 contains ingredient1 (color: red).- Dispenser2 contains ingredient2 (color: blue).- Left hand is holding shot1.- Right hand is holding shot2.

Rank 4: State ID 10
State Description: - Shot1 is on the table, contains ingredient1, used.- Shot2 is clean and empty on the table.- Shot3 is clean and empty on the table.- Shaker1 is clean, empty, and at fill level l0 on the table.- Dispenser1 contains ingredient1 (color: red).- Dispenser2 contains ingredient2 (color: blue).- Left hand is empty.- Right hand is empty.

Rank 5: State ID 12
State Description: - Shot1 is clean, contains ingredient2, and is on the table.- Shot2 is clean and empty on the table.- Shot3 is clean and empty on the table.- Shaker1 is clean, empty, and at fill level l0 on the table.- Dispenser1 contains ingredient1 (color: red).- Dispenser2 contains ingredient2 (color: blue).- Left hand is empty.- Right hand is empty.

Rank 6: State ID 15
State Description: - Shot_1: Clean, empty, on the table.- Shot_2: Clean, empty, on the table.- Shot_3: Clean, empty, held by right hand.- Shaker_1: Contains ingredient1, not clean, fill level l1, held by left hand.- Dispenser_1: Contains ingredient1 (red), used to fill shaker_1.- Dispenser_2: Contains ingredient2 (blue).- Left_hand: Holding shaker_1 with ingredient1.- Right_hand: Holding shot_3.- Cocktail_1: Defined by mixing ingredient1 and ingredient2.- Cocktail_2: Defined by mixing ingredient1 and ingredient2.

Rank 7: State ID 16
State Description: - Shot_1: Clean, empty, held by right hand.- Shot_2: Clean, empty, on the table.- Shot_3: Clean, empty, on the table.- Shaker_1: Contains ingredient1, not clean, fill level l1, held by left hand.- Dispenser_1: Contains ingredient1 (red), used to fill shaker_1.- Dispenser_2: Contains ingredient2 (blue).- Left_hand: Holding shaker_1 with ingredient1.- Right_hand: Holding shot_1.- Cocktail_1: Defined by mixing ingredient1 and ingredient2.- Cocktail_2: Defined by mixing ingredient1 and ingredient2.

Rank 8: State ID 13
State Description: - Shot_1: Held by left_hand, clean, empty.- Shot_2: Clean, empty, on the table.- Shot_3: Clean, empty, on the table.- Shaker_1: Clean, empty, fill level l0, on the table.- Dispenser_1: Contains ingredient1 (red).- Dispenser_2: Contains ingredient2 (blue).- Left_hand: Holding shot_1.- Right_hand: Empty.- Cocktail_1: Defined by mixing ingredient1 and ingredient2.- Cocktail_2: Defined by mixing ingredient1 and ingredient2.

