
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
Given that the number $120n^3$ has $120$ positive integer divisors, determine how many positive integer divisors the number $16n^5$ has, where $n$ is a positive integer.

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