
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
The function $f(x) = 4\cos(\omega x - \frac{\pi}{6})\sin\omega x - 2\cos(2\omega x + \pi)$, where $\omega > 0$.
(1) Find the range of the function $y = f(x)$;
(2) If the smallest positive period of $f(x)$ is $\pi$, find the intervals of increase for $f(x)$ in the interval $\left[-\frac{\pi}{2}, \pi\right]$.

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