
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 $f(x)=2 \sqrt{3}\sin x\cos x+2\cos ^{2}x-1(x∈R)$.
(1) Find the smallest positive period of the function $f(x)$ and its maximum and minimum values in the interval $\left[ 0, \dfrac{π}{2} \right]$.
(2) If $f({x}_{0})= \dfrac{6}{5} $, $({x}_{0})∈\left[ \dfrac{π}{4}, \dfrac{π}{2} \right]$, find the value of $\cos 2{x}_{0}$.

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