
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

To encrypt texts, the famous Swiss mathematician Leonhard Euler (1707-1783) used Latin squares. A partially filled Latin square with four rows and four columns is given in the table.

| 1 | 2 | 3 | 4 |
| - | - | - | - |
| 2 |   |   |   |
| 3 |   |   |   |
| 4 |   |   |   |

Fill in the remaining cells in the table such that each number 1, 2, 3, and 4 appears exactly once in each row and each column. Try to find as many different solutions as possible.

Present the answer in LaTex format: \boxed{Your answer}
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