
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
Find all possible pairs of positive integers \((m, n)\) such that if you draw \(n\) lines which intersect in \(\frac{n(n-1)}{2}\) distinct points and \(m\) parallel lines which meet the \(n\) lines in a further \(mn\) distinct points (distinct from each other and from the first \(\frac{n(n-1)}{2}\) points), then exactly 1992 regions are formed.

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