
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: $\overrightarrow{a}=(2\cos x,\sin x)$, $\overrightarrow{b}=( \sqrt {3}\cos x,2\cos x)$, and the function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b} - \sqrt {3} (x \in \mathbb{R})$. Find:
(1) The smallest positive period of $f(x)$;
(2) The interval(s) where $f(x)$ is monotonically increasing.

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