
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 vectors $m=(2\sin \omega x, \cos^2 \omega x - \sin^2 \omega x)$ and $n=(\sqrt{3}\cos \omega x, 1)$, where $\omega > 0$ and $x \in R$. If the smallest positive period of the function $f(x)=m \cdot n$ is $\pi$.

(1) Find the value of $\omega$;

(2) In $\triangle ABC$, if $f(B)=-2$, $BC= \sqrt{3}$, $\sin B= \sqrt{3}\sin A$, find the value of $\overrightarrow{BA} \cdot \overrightarrow{BC}$.

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