
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 all positive integers \( n > 1 \) such that any positive divisor of \( n \) greater than 1 has the form \( a^r + 1 \), where \( a \) is a positive integer and \( r \) is a positive integer greater than 1.

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