
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
Find all positive integers $n$ that satisfy the following conditions:
(1) $n$ has at least 4 positive divisors.
(2) If $d_{1}<d_{2}<\cdots<d_{k}$ are all the positive divisors of $n$, then $d_{2}-d_{1}, d_{3}-d_{2}, \cdots, d_{k}-d_{k-1}$ form a geometric sequence.

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