
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-2\cos x $.

(1) Find the maximum and minimum values of $f(x)$ when $x\in [0,\pi]$.

(2) If $f(x)=0$, find the value of $\frac{2\cos^{2} \frac{x}{2}-\sin x-1}{\sqrt{2}\sin \left(x+ \frac{\pi}{4}\right)}$.

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