
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
For a positive integer  $n$  consider all its divisors  $1 = d_1 < d_2 < \ldots < d_k = n$ . For  $2 \le i \le k-1$ , let's call divisor  $d_i$  good, if  $d_{i-1}d_{i+1}$  isn't divisible by  $d_i$ . Find all  $n$ , such that the number of their good divisors is smaller than the number of their prime distinct divisors.

*Proposed by Mykhailo Shtandenko*

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