
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 $f(x)=2\sin x\cos x+2\sqrt{3}\cos^{2}x-\sqrt{3}$.
(1) Find the interval(s) where the function $f(x)$ is decreasing;
(2) Translate the graph of the function $y=f(x)$ to the left by $\frac{\pi}{6}$ units, then compress the $x$-coordinates of all points on the resulting graph to $\frac{1}{2}$ of their original length (without changing the $y$-coordinates) to obtain the graph of the function $y=g(x)$. Find the range of $y=g(x)$ on the interval $(-\frac{\pi}{12},\frac{\pi}{8})$.

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