
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
How many different $5 \times 5$ arrays whose entries are 1's, -1's, and 0's have the property that the sum of the entries in each row is 0, the sum of the entries in each column is 0, and each row and column should contain exactly one 0?

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