
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
At the initial moment, a positive integer \( N \) is written on the blackboard. In each step, Misha can choose a positive integer \( a > 1 \) written on the blackboard, erase it, and write all its positive divisors except itself. It is known that after several steps, there are exactly \( N^{2} \) numbers on the blackboard. Find all possible values of \( N \).

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