
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
Every cell of an $8\times8$ chessboard contains either $1$ or $-1$. Given that there are at least four rows such that the sum of numbers inside the cells of those rows is positive, determine the maximum number of columns such that the sum of numbers inside the cells of those columns is less than $-3$.

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