
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
Let \( A \) be a set of any 100 distinct positive integers. Define
\[ B = \left\{ \left.\frac{a}{b} \right|\, a, b \in A \text{ and } a \neq b \right\}, \]
and let \( f(A) \) denote the number of elements in the set \( B \). What is the sum of the maximum and minimum values of \( f(A) \)?

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