
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 $f(x)=\frac{\sqrt{3}}{2}\sin 2x-\cos^{2}x-\frac{1}{2}$.

(I) Find the smallest positive period and the interval where the function is monotonically increasing.

(II) When $x\in\left[-\frac{\pi}{12},\frac{5\pi}{12}\right]$, find the minimum and maximum values of the function $f\left(x\right)$.

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