
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 $f(x) = 4\tan(x) \sin(\frac{\pi}{2} - x)\cos(x - \frac{\pi}{3}) - \sqrt{3}$,
(1) Find the smallest positive period of $f(x)$ __________;
(2) Find the intervals in which $f(x)$ is monotonically increasing __________.

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