
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 pairs \((a, b)\) of positive integers such that \(a^3\) is a multiple of \(b^2\) and \(b-1\) is a multiple of \(a-1\). Note: An integer \(n\) is said to be a multiple of an integer \(m\) if there is an integer \(k\) such that \(n=km\).

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