
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 the derivative of the function $f(x)$ is $f'(x) = 2 + \sin x$, and $f(0) = -1$. The sequence $\{a_n\}$ is an arithmetic sequence with a common difference of $\frac{\pi}{4}$. If $f(a_2) + f(a_3) + f(a_4) = 3\pi$, calculate $\frac{a_{2016}}{a_{2}}$.

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