
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
Consider all the positive integers  $N$  with the property that all of the divisors of  $N$  can be written as  $p-2$  for some prime number  $p$ . Then, there exists an integer  $m$  such that  $m$  is the maximum possible number of divisors of all
numbers  $N$  with such property. Find the sum of all possible values of  $N$  such that  $N$  has  $m$  divisors.

*Proposed by **FedeX333X***

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