
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 the function $f(x)=\sin ^{2}x+ \sqrt {3}\sin x\cos x- \frac {1}{2}$,
(1) Find the range of the function $f(x)$ when $x\in[0, \frac {\pi}{2}]$;
(2) Given that $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ of $\triangle ABC$ respectively, where $A$ is an acute angle, $a=2 \sqrt {3}$, $c=4$ and $f(A)=1$, find $A$, $b$ and the area $S$ of $\triangle ABC$.

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