
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) When $x \in \left[0, \frac{\pi}{2}\right]$, find the range of $f(x)$.

(2) If $\triangle ABC$ has internal angles $A$, $B$, $C$ opposite to sides $a$, $b$, $c$ respectively, and it satisfies $\frac{b}{a} = \sqrt{3}$, $\frac{\sin(2A+C)}{\sin A} = 2 + 2\cos(A+C)$, find the value of $f(B)$.

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