
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
Cells of an $n \times n$ square table $(n \geqslant 3)$ are filled with the numbers $\pm 1$ according to the following rules:
1) All border cells of the table are filled with the number -1;
2) The number placed in each subsequent empty cell of the table, which can be chosen arbitrarily, is equal to the product of the nearest numbers to this cell, located on either side of it, in the same row or in the same column as it. This continues until all empty cells of the table are filled.
a) What is the maximum, 
b) the minimum number of +1s that can appear in the table?

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