
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

Sasha chose a natural number \( N > 1 \) and listed all its natural divisors in ascending order: \( d_{1} < \ldots < d_{s} \) (such that \( d_{1} = 1 \) and \( d_{s} = N \)). Then, for each pair of adjacent numbers, he calculated their greatest common divisor; the sum of these \( s-1 \) numbers turned out to be \( N-2 \). What values could \( N \) take?

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