
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 $6\times 6$ arrays whose entries are all 1's and -1's have the property that the sum of the entries in each row and each column is 0, and additionally the sum of the entries in every two adjacent rows and every two adjacent columns is also 0?

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