
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
To determine the number of positive divisors of a number, you simply factor it as powers of distinct primes and multiply the successors of the exponents. For example, \(2016=2^{5} \cdot 3^{2} \cdot 5^{1}\) has \((5+1)(2+1)(1+1)=36\) positive divisors. Consider the number \(n=2^{7} \cdot 3^{4}\).

a) Determine the number of positive divisors of \(n^{2}\).

b) How many divisors of \(n^{2}\) are greater than \(n\)?

c) How many divisors of \(n^{2}\) are greater than \(n\) and are not multiples of \(n\)?

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