
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, define \( f(n) \) as the quotient obtained when the sum of all positive divisors of \( n \) is divided by \( n \). Calculate \( f(540) - f(180) \).
**A)** \( \frac{1}{90} \)
**B)** \( \frac{1}{45} \)
**C)** \( \frac{7}{90} \)
**D)** \( 1 \)
**E)** \( \frac{8}{45} \)

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