
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 $f(x)=\sqrt{3}\sin(\omega x+\varphi)+2\sin^{2}\frac{\omega x+\varphi}{2}-1(\omega > 0,0 < \varphi < \pi)$, the distance between adjacent symmetry axes is $\frac{\pi}{2}$, and $f(0)=0$.
(1) Find the analytical expression of $f(x)$;
(2) Translate the graph of the function $y=f(x)$ to the right by $\frac{\pi}{6}$ units, then shrink the abscissa to half of its original length (the ordinate remains unchanged) to obtain the graph of the function $y=g(x)$. Find the range of $g(x)$ when $x\in[-\frac{\pi}{12},\frac{\pi}{6}]$.

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