
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 $f(x)= \sqrt{3}\sin ⁡ωx−2{(\sin ⁡ \dfrac{ωx}{2})}^{2}(ω > 0)$ with the smallest positive period of $3π$.

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

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

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