
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
Determine all composite positive integers  $n$  with the following property: If  $1 = d_1 < d_2 < \cdots < d_k = n$  are all the positive divisors of  $n$ , then  $$ (d_2 - d_1) : (d_3 - d_2) : \cdots : (d_k - d_{k-1}) = 1:2: \cdots :(k-1) $$  (Walther Janous)

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