
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 the number of integers  $n$  with  $1\le n\le 100$  for which  $n-\phi(n)$  is prime.  Here  $\phi(n)$  denotes the number of positive integers less than  $n$  which are relatively prime to  $n$ .

*Proposed by Mehtaab Sawhney*

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