
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
For a positive integer \( n \), let \( \varphi(n) \) denote the number of positive integers less than or equal to \( n \) that are coprime to \( n \). Let \( f(n) \) denote the smallest positive integer greater than \( n \) that is not coprime to \( n \). If \( f(n) = m \) and \( \varphi(m) = n \), then the pair of positive integers \( (n, m) \) is called a friendly pair. Find all friendly pairs.

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