
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 $n.$ Calculate $f(1024) - f(512)$, where $1024 = 2^{10}$ and $512 = 2^9$.
A) $\frac{1}{2048}$
B) $\frac{1}{1024}$
C) $\frac{1}{512}$
D) $\frac{1}{256}$
E) $\frac{1}{128}$

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