
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 $f(x)=2 \sqrt {3}\sin x\cos x-\cos 2x$, where $x\in R$.
(1) Find the interval where the function $f(x)$ is monotonically increasing.
(2) In $\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $f(A)=2$, $C= \frac {\pi}{4}$, and $c=2$, find the value of the area $S_{\triangle ABC}$.

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