
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 $a= \int_{0}^{1} (e^x+2x)dx$ (where $e$ is the base of the natural logarithm), and the function $f(x)= \begin{cases} \ln x, & x>0 \\ 2^{-x}, & x\leq 0 \end{cases}$, then $f(a)+f(\log_{2} \frac{1}{6})=$ ______.

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