
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 $5 \times 5$ matrix, each element is either 0 or 1, and it satisfies the following conditions: the sum of the elements in each of the five rows is equal, but the sum of the elements in each of the five columns is pairwise different. Find the number of such matrices.

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