
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
Consider $a = 2^{10} \cdot 5^2$ and $b = 2^9 \cdot 5^2$. Compute $f(a) - f(b)$ where $f(n)$ represents the ratio of the sum of all positive divisors of $n$ to $n$.
A) $\frac{1}{2560}$
B) $\frac{31}{3200}$
C) $\frac{62}{3200}$
D) $\frac{1}{160}$

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