
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 $\vec{a}=(\sin x, \frac{1}{2})$ and $\vec{b}=(\sqrt{3}\cos x + \sin x, -1)$, define the function $f(x) = \vec{a} \cdot \vec{b}$.
(1) Find the smallest positive period of the function $f(x)$.
(2) Determine the maximum and minimum values of $f(x)$ in the interval $\left[\frac{\pi}{4}, \frac{\pi}{2}\right]$.

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