
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
There is number  $N$  on the board. Every minute Ivan makes next operation: takes any number  $a$  written on the board, 
 erases it, then writes all divisors of  $a$  except  $a$ ( Can be same numbers on the board). After some time on the board there are  $N^2$  numbers.
For which  $N$  is it possible?

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