
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
Let \( n \) be a positive integer, \(\varphi(n)\) denote the number of positive integers less than or equal to \( n \) that are coprime to \( n \), and \(\tau(n)\) denote the number of positive divisors of \( n \). Find all positive integers \( n \) with exactly two distinct prime factors such that
\[
\varphi(\tau(n)) = \tau(\varphi(n)).
\]

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