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

(1) Find the smallest positive period of the function $f(x)$ and its maximum and minimum values in the interval $[0,\frac{\pi }{2}]$.

(2) If $f(x_{0})=\frac{6}{5}, (x_{0}\in [\frac{\pi }{4},\frac{\pi }{2}])$, find the value of $\cos 2x_{0}$.

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