
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 that the minimum positive period of the function $f(x) = \sqrt{3} \sin(\pi + \omega x) \sin(\frac{3\pi}{2} - \omega x) - \cos^{2} \omega x \ (\omega > 0)$ is $T = \pi$.
(1) Find the value of $f(\frac{2\pi}{3})$;
(2) In $\triangle ABC$, the sides corresponding to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $(2a - c) \cos B = b \cos C$, find the measure of angle $B$ and the range of $f(A)$.

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