
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 vectors $\overrightarrow{m}=( \sqrt {3}\sin x-\cos x,1)$ and $\overrightarrow{n}=(\cos x, \frac {1}{2})$, and the function $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}$,
(1) Find the interval(s) where the function $f(x)$ is monotonically increasing;
(2) If $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ of $\triangle ABC$, $a=2 \sqrt {3}$, $c=4$, and $f(A)=1$, find the area of $\triangle ABC$.

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