
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 each positive integer \( n \), let \( g_1(n) \) be thrice the number of positive integer divisors of \( n \), and for \( j \ge 2 \), let \( g_j(n) = g_1(g_{j-1}(n)) \). For how many values of \( n \le 100 \) is \( g_{30}(n) = 18 \)?
A) 0
B) 1
C) 2
D) 3

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