
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
Let  $N$  be a positive integer; a divisor of  $N$  is called *common* if it's great than  $1$  and different of  $N$ . A positive integer is called *special* if it has, at least, two common divisors and it is multiple of all possible differences between any two of their common divisors. 
Find all special integers.

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