
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 rectangular table has every entry a positive integer. \( n \) is a fixed positive integer. A move consists of either subtracting \( n \) from every element in a column or multiplying every element in a row by \( n \). Find all \( n \) such that we can always end up with all zeros whatever the size or content of the starting table.

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