
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 $f(x)= \sqrt{3}\sin (\pi+\omega x)\sin \left( \dfrac{3\pi}{2}-\omega x\right)-\cos ^{2}\omega x (\omega > 0)$ has the smallest positive period of $T=\pi$.

(Ⅰ) Find the value of $f\left( \dfrac{2\pi }{3} \right)$;

(Ⅱ) In $\Delta ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $(2a-c)\cos B=b\cos C$, find the size of angle $B$ and the range of values for $f(A)$.

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