
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 vectors $$\overrightarrow{a} = (\sin x, -2\cos x)$$ and $$\overrightarrow{b} = (\sin x + \sqrt{3}\cos x, -\cos x)$$, where $x \in \mathbb{R}$. Let the function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$.
(1) Find the smallest positive period of the function $f(x)$.
(2) Find the maximum and minimum values of the function $f(x)$ in the interval $$[0, \frac{\pi}{2}]$$.

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