
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 $a$ and $b$ are the sides opposite to angles $A$ and $B$ respectively in $\triangle ABC$, and $b\sin ^{2}A= \sqrt {3}a\cos A\sin B$. The function is defined as $f(x)=\sin A\cos ^{2}x-\sin ^{2} \frac {A}{2}\sin 2x$, where $x\in[0, \frac {\pi}{2}]$.

1. Find $A$
2. Find the range of the function $f(x)$.

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