
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 $f\left(x\right)=\sqrt{3}\sin \left(\omega x+\varphi \right)$ ($\omega\ \ \gt 0$, $-\frac{π}{2}\leqslant \varphi\ \ \lt \frac{π}{2}$), whose graph is symmetric about the line $x=\frac{π}{3}$, and the distance between two adjacent highest points on the graph is $\pi$. <br/>$(Ⅰ)$ Find the values of $\omega$ and $\varphi$; <br/>$(Ⅱ)$ If $f(\frac{α}{2})=\frac{\sqrt{3}}{4}$ ($\frac{π}{6} \lt \alpha\ \ \lt \frac{2π}{3}$), find the value of $\cos (\alpha +\frac{3π}{2})$.

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