
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
Suppose \( m \) and \( n \) are integers with \( 0 < m < n \). Let \( P = (m, n) \), \( Q = (n, m) \), and \( O = (0,0) \). For how many pairs of \( m \) and \( n \) will the area of triangle \( OPQ \) be equal to 2024?

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