
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 functions $f(x)$ and $g(x)$ both have a domain of $R$. $f(x)$ is an odd function and satisfies $g(x)=f(x+\frac{1}{6})$, $g(x+\frac{1}{3})=f(\frac{1}{2}-x)$. On the interval $(0,\frac{1}{2})$, $f(x)=2^{x}-1$. Find $f(\log_{2}5)+g(\frac{5}{6})$.

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