
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 $f(x)=2\sqrt{3}\sin x\cos x-3\sin^{2}x-\cos^{2}x+3$.

(1) Find the range of $f(x)$ when $x\in(0,\frac{\pi}{2})$.

(2) In triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and they satisfy $\frac{b}{a}=\sqrt{3}$, $\frac{\sin (2A+C)}{\sin A}=2+2\cos (A+C)$. Find the value of $f(B)$.

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