
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
Define a function \( f(x) \) on \( \mathbb{R} \) that satisfies \( f(-x) = -f(x) \), \( f(x-2) = f(x+2) \), and when \( x \in (-1,0) \), \( f(x) = 2^x + \frac{1}{5} \). Then, evaluate \( f(\log_{2} 20) \).

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