
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 $f(n)$ be the quotient obtained when the sum of all positive divisors of $n$ is divided by $n.$ For example, \[f(18)=(1+2+3+6+9+18)\div 18=\frac{39}{18}\]
What is $f(960)-f(480)?$
A) $\frac{1}{960}$
B) $\frac{1}{240}$
C) $\frac{1}{120}$
D) $\frac{1}{40}$
E) $\frac{1}{10}$

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