
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 $f(x)=4\cos ωx\sin \left(wx- \frac{π}{6}\right)$ $(ω > 0)$ with the smallest positive period of $π$.

(1) Find $ω$;

(2) In triangle $△ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. It is known that the acute angle $A$ is a zero point of the function $f(x)$, and $\sin B= \sqrt{3}\sin C$, the area of $△ABC$ is $S=2\sqrt{3}$, find $a$.

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