
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
Given the operation "$f$", if $f(1) = 2, f(2) = 4, f(3) = 6 \ldots$, $f(\frac{1}{2}) = 2, f(\frac{1}{3}) = 3, f(\frac{1}{4}) = 4 \ldots$, calculate $f(2022) - f(\frac{1}{2022})$.

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