
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
Determine all pairs of positive integers \((m, n)\) for which it is possible to place some stones in the cells of a board with \(m\) rows and \(n\) columns, with no more than one stone per cell, such that all columns have the same number of stones, and no two rows have the same number of stones.

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