
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 each natural number  $a$  we denote  $\tau (a)$  and  $\phi (a)$  the number of natural numbers dividing  $a$  and the number of natural numbers less than  $a$  that are relatively prime to  $a$ . Find all natural numbers  $n$  for which  $n$  has exactly two different prime divisors and  $n$  satisfies  $\tau (\phi (n))=\phi (\tau (n))$ .

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