
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 \( n = p_{1} p_{2} \cdots p_{k} \) which divide \( \left( p_{1} + 1 \right) \left( p_{2} + 1 \right) \cdots \left( p_{k} + 1 \right) \), where \( p_{1} p_{2} \cdots p_{k} \) is the factorization of \( n \) into prime factors (not necessarily distinct). The answer should be described in terms of conditions on the exponents.

### Answer
All numbers \( 2^{r} 3^{s} \) where \( r \) and \( s \) are non-negative integers and \( s \leq r \leq 2 s \).

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