
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 that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively in an acute triangle $\triangle ABC$, and $(a+b)(\sin A-\sin B)=(c-b)\sin C$.

(I) Find the measure of $\angle A$;

(II) If $f(x)= \sqrt{3}\sin \frac{x}{2}\cdot\cos \frac{x}{2}+\cos^{2} \frac{x}{2}$, find the range of $f(B)$.

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