
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
Given a \(4 \times 4\) grid where each cell contains a unique number from 1 to 16, the numbers in each row and column increase from left to right and from top to bottom with 1 in the top left corner and 16 in the bottom right corner, calculate the number of such grids possible.

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