
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 $f(x) = \frac{1}{2} \sin 2x - \sqrt{3} \cos ^{2}x$.

(1) Find the smallest positive period and minimum value of $f(x)$;

(2) Stretch the horizontal coordinate of each point on the graph of the function $f(x)$ to twice its original length, and the vertical coordinate remains unchanged to obtain the graph of the function $g(x)$. When $x \in [\frac{\pi}{2}, \pi]$, find the range of $g(x)$.

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