
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 \( n > 1 \) with the following property:

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

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