
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 $f(x) = \sqrt{3}\sin \omega x \cdot \cos \omega x - \cos^2 \omega x$ $(\omega > 0)$ has a period of $\frac{\pi}{2}$.

(1) Find the value of $\omega$ and the intervals of monotonic increase for the function $f(x)$;

(2) Suppose the sides $a$, $b$, $c$ of $\triangle ABC$ satisfy $b^2=ac$, and the angle opposite to side $b$ is $x$, find the range of the function $f(x)$ under this condition.

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