
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
Let \( g(n) \) be the product of the proper positive integer divisors of \( n \). For how many values of \( n \) does \( n \) not divide \( g(n) \), given that \( 2 \le n \le 100 \), and also considering when \( n \) is the cube of a prime?

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