
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: Let $1 = d_1 < d_2 < \ldots < d_k = n$ be all the positive divisors of $n$. Then:

$$
\left(d_{2} - d_{1}\right) : \left(d_{3} - d_{2}\right) : \cdots : \left(d_{k} - d_{k-1}\right) = 1 : 2 : \cdots : (k - 1).
$$

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