
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 positive integer \( n \), fill an \( n \times n \) grid with the numbers \( 1, 2, 3, \ldots, n^2 \) such that each number appears exactly once. The grid is called "excellent" if the sum of the numbers in any row or any column is the same. Find the maximum number of "excellent" grids.

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