
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 $f(x)=4\sin \omega x\cos (\omega x+\dfrac{\pi }{3})+2\sqrt{3}(\omega > 0)$.

(1) If the smallest positive period of $f(x)$ is $\pi$, find the maximum and minimum values of $f(x)$ in the interval $[\dfrac{-\pi }{4},\dfrac{\pi }{6}]$ and the values of $x$ when these extreme values are attained.

(2) If $y=f(x)$ is an increasing function in the interval $[\dfrac{-\pi }{4},\dfrac{\pi }{6}]$, find the maximum value of $\omega$.

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