
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
For all integers  $n\ge 2$  with the following property:



- for each pair of positive divisors  $k,~\ell <n$ , at least one of the numbers  $2k-\ell$  and  $2\ell-k$  is a (not necessarily positive) divisor of  $n$  as well.


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