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

(I) Find the value of $\omega$.

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

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