
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
The divisors of a natural number \( n \) (including \( n \) and 1) which has more than three divisors, are written in ascending order: \( 1 = d_{1} < d_{2} < \ldots < d_{k} = n \). The differences \( u_{1} = d_{2} - d_{1}, u_{2} = d_{3} - d_{2}, \ldots, u_{k-1} = d_{k} - d_{k-1} \) are such that \( u_{2} - u_{1} = u_{3} - u_{2} = \ldots = u_{k-1} - u_{k-2} \). Find all such \( n \).

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