
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
If the function $f(x)=A\sin(\omega x+\varphi)$ $(A>0$, $\omega>0$, $|\varphi|<\frac{π}{2})$ has a minimum value of $-2$ and its graph passes through the points $(0,\sqrt{3})$ and $(\frac{5π}{6},0)$, and the function $f(x)$ is monotonically increasing on $[0,\frac{π}{6}]$. <br/>$(I)$ Find the analytical expression of $f(x)$; <br/>$(II)$ If $x\in [0,\frac{5π}{8}]$, find the range of $f(x)$.

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