
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  $n=p_1p_2 \cdots p_k$  which divide  $(p_1+1)(p_2+1)\cdots (p_k+1)$  where  $p_1 p_2 \cdots p_k$  is the factorization of  $n$  into prime factors (not necessarily all distinct).

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