
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 positive integer triples \((a, m, n)\) that satisfy the following conditions: \(a > 1,\ m < n,\) and the set of prime factors of \(a^m - 1\) is the same as the set of prime factors of \(a^n - 1\).

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