
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
 $n$  is composite.  $1<a_1<a_2<...<a_k<n$  - all divisors of  $n$ . It is known, that  $a_1+1,...,a_k+1$  are all divisors for some  $m$  (except  $1,m$ ). Find all such  $n$ .

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