
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 $f(x) = \sqrt{3}\sin\omega x - 2\sin^2\frac{\omega x}{2} \ (\omega > 0)$ is $3\pi$.

(1) Find the minimum value of the function $f(x)$ when $x \in [\frac{\pi}{2}, \frac{3\pi}{4}]$;

(2) In $\Delta ABC$, if $f(C) = 1$ and $2\sin 2B = \cos B + \cos (A - C)$, find the value of $\sin A$.

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