
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
A $7 \times 7$ table is filled with non-zero integers. Initially, the border of the table is filled with negative numbers. Next, the cells are filled in any order, and the next number is equal to the product of the previously placed numbers closest to it either in the row or column. What is the maximum number of positive numbers that can be in the table?

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