
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 the positive integers  $n$  such that: $(1)$   $n$  has at least  $4$  positive divisors. $(2)$  if all positive divisors of  $n$  are  $d_1,d_2,\cdots ,d_k,$  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}
user