
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
In a $3 \times 3$ grid, there are four $2 \times 2$ subgrids. Kasun wants to place an integer from 1 to 4 inclusive in each cell of the $3 \times 3$ grid so that every $2 \times 2$ subgrid contains each integer exactly once. For example, the grid below on the left satisfies the condition, but the grid below on the right does not. In how many ways can Kasun place integers in the grid so that they satisfy the condition?

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

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

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