
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]


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Define a function $f(x)$ on $\mathbb{R}$ which satisfies $f(-x) = -f(x)$ and $f(x-4) = f(x)$. Given that $f(x) = 2^x + \frac{1}{5}$ for $x \in (-1,0)$, determine the value of $f(\log_{2}{20})$.

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