
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 $f(x)=\sqrt{3}\sin (\omega x+\varphi )$ $(\omega > 0,-\dfrac{\pi }{2}\leqslant \varphi \leqslant \dfrac{\pi }{2})$ whose graph is symmetric about the line $x=\dfrac{\pi }{3}$, and the distance between two adjacent highest points on the graph is $\pi$.

$(1)$ Find the values of $\omega$ and $\varphi$;

$(2)$ If $f\left(\dfrac{\alpha }{2}\right)=\dfrac{\sqrt{3}}{4}$ $(\dfrac{\pi }{6} < \alpha < \dfrac{2\pi }{3})$, find the value of $\sin \alpha$

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