
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
The function $f(x)$ is defined on $\mathbb{R}$ and satisfies the equations $f(-x) + f(x) = 0$ and $f(x+4) = f(x)$. When $x \in (-2, 0)$, $f(x) = 2^x + \frac{1}{5}$. Find the value of $f(\log_{2} 20)$.

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