
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
Given that \(a\) and \(b\) are positive integers, \(a < b\), and \(a\) and \(b\) are coprime. If the inequality \(a x + b y \leq a b\) has exactly 2023 positive integer solutions for \(x\) and \(y\), what are the possible pairs \((a, b)?\) Find all possible pairs that satisfy the given conditions.

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