
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 an integer greater than 1, and its positive divisors be \( d_1, d_2, \cdots, d_k \) where \( 1 = d_1 < d_2 < \cdots < d_k = n \). It is known that \( d_2 - d_1, d_3 - d_2, \cdots, d_k - d_{k-1} \) are all the positive divisors of another positive integer (all distinct but not necessarily in increasing order). Find all possible values of \( n \).

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