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

(I) Find the interval(s) where $f(x)$ is monotonically increasing.

(II) When $x\in [-\pi ,0]$, find the maximum and minimum values of $f(x)$ and their corresponding $x$ values.

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