
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 $f\left(x\right)=\sqrt{3}\sin(\omega x+\varphi)$ ($\omega>0$, $-\frac{\pi}{2}<\varphi<\frac{\pi}{2}$), where $A\left(\frac{1}{3},0\right)$ is the center of symmetry of its graph, $B$ and $C$ are the adjacent highest and lowest points on the graph, respectively. If $BC=4$, then the analytical expression of $f\left(x\right)$ is ____.

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