
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 an $n \times n$ grid ($n \geq 3$), fill in each cell according to the following rules:
1. Every cell on the edge of the grid is filled with -1.
2. For any empty cell, fill it with the product of the two nearest filled cells in its row or column.

Continue this process until all cells in the grid are filled. Determine:
(i) The maximum number of +1s that can appear in the grid.
(ii) The minimum number of +1s that can appear in the grid.

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