
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 function $f(x)=2\cos ^{2} \frac{x}{2}+ \sqrt {3}\sin x$.
(I) Find the maximum value of the function $f(x)$, and write out the corresponding set of values of $x$ when the maximum value is obtained;
(II) If $\tan \frac {α}{2}= \frac {1}{2}$, find the value of $f(α)$.

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