
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 \(n\) a positive integer, let \(g(n)\) be the quotient obtained when the product of all positive divisors of \(n\) is divided by \(n\). Given that:
\[ g(20) = \left(1 \cdot 2 \cdot 4 \cdot 5 \cdot 10 \cdot 20\right) \div 20 \]
What is \(g(180) - g(90)?\)
A) \(180^8 - 90^5\)
B) \(180^8\)
C) \(90^5\)
D) \(180^8 + 90^5\)
E) \(2\)

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