
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: $f(x)=2 \sqrt {3}\cos ^{2}x+ \sin 2x - \sqrt {3}+1 (x \in R)$. Find:
(I) The smallest positive period of $f(x)$;
(II) The interval(s) where $f(x)$ is monotonically increasing;
(III) The range of $f(x)$ when $x \in [- \frac{\pi}{4}, \frac{\pi}{4}]$.

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