
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 $\overrightarrow{m}=(2\sin x,\sin x-\cos x)$, $\overrightarrow{n}=( \sqrt {3}\cos x,\sin x+\cos x)$, let $f(x)= \overrightarrow{m} \cdot \overrightarrow{n}$.
(1) Find the set of all possible values of $x$ when the function $f(x)$ reaches its maximum value.
(2) In triangle $ABC$, if $f(C)=2$, $c= \sqrt {3}$, find the maximum area of triangle $ABC$.

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