
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
In $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$, respectively. $S$ is the area of $\triangle ABC$, and $4S= \sqrt {3}(a^{2}+b^{2}-c^{2})$.
(1) Find the measure of angle $C$.
(2) $f(x)=4\sin x\cos (x+ \frac {\pi}{6})+1$. When $x=A$, $f(x)$ attains its maximum value $b$. Find the value of $S$.

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