
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 $f(x) = 4 \tan x \sin (\frac{\pi}{2} - x) \cos (x - \frac{\pi}{3}) - \sqrt{3}$.
(I) Find the smallest positive period of $f(x)$;
(II) Find the interval(s) on which $f(x)$ is monotonically increasing in $[- \frac{\pi}{4}, \frac{\pi}{4}]$.

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