
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 $a,b$ are the sides opposite to angles $A,B$ respectively of $\Delta ABC$, and $b\sin^{2}A=\sqrt{3}a\cos A\sin B$, with the function $f(x)=\sin A\cos^{2}x-\sin^{2}\frac{A}{2}\sin 2x, x\in \left[ 0,\frac{\pi }{2} \right]$.

(I) Find $A$;

(II) Find the range of the function $f(x)$.

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