
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 function $f(x) = \frac{2^{2x}}{2+2^{2x}}$:

1. Find $f(\frac{1}{2})$;
2. Find the value of $f(x) + f(1-x)$;
3. Find the value of $f(\frac{1}{100}) + f(\frac{2}{100}) + f(\frac{3}{100}) + \dots + f(\frac{98}{100}) + f(\frac{99}{100})$.

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