
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
It is known that for every integer  $n > 1$  there is a prime number among the numbers  $n+1,n+2,...,2n-1.$  Determine all positive integers  $n$  with the following property: Every integer  $m > 1$  less than  $n$  and coprime to  $n$  is prime.




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