
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]


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In $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and $b\cos C+c\cos B=2a\cos B$.

(I) Find the measure of angle $B$;

(II) Given the function $f\left( x \right)=\sin \left( 2x+B \right)+\sin \left( 2x-B \right)+2{{\cos }^{2}}x-1,x\in R$.

(1) Find the smallest positive period of the function $f\left( x \right)$;

(2) Find the maximum and minimum values of the function $f\left( x \right)$ on the interval $\left[ -\dfrac{\pi }{4},\dfrac{\pi }{4} \right]$.

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