
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 $f(x)=\sqrt{3}\sin \omega x-2\sin^{2}\frac{\omega x}{2}\ (\omega > 0)$ with the smallest positive period of $3\pi$.

(1) Find the maximum and minimum values of the function $f(x)$ in the interval $\left[-\frac{3\pi}{4}, \pi \right]$.

(2) Let $a, b, c$ be the sides opposite to angles $A, B, C$, respectively, in an acute triangle $ABC$, and satisfy $b=2$, $f(A)=\sqrt{3}-1$, $\sqrt{3}a=2b\sin A$. Find the area of $\triangle ABC$.

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