
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  $A_n$  be the set of all positive numbers greater than  $1$  and less than  $n$  which are coprime to  $n$ . Find all  $n$  such that all the elements of  $A_n$  are prime numbers.

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