
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 $$\overrightarrow {m} = (2\cos x + 2\sqrt {3}\sin x, 1)$$, $$\overrightarrow {n} = (\cos x, -y)$$, and $$\overrightarrow {m}$$ is perpendicular to $$\overrightarrow {n}$$.
(1) Express $y$ as a function of $x$, denoted as $f(x)$, and find the interval of $x$ where $f(x)$ is monotonically increasing;
(2) Given that $a$, $b$, and $c$ are the lengths of the sides opposite to angles $A$, $B$, and $C$ in $\triangle ABC$ respectively, if $f\left(\frac{A}{2}\right) = 3$, and $a=2$, $b+c=4$, find the area of $\triangle ABC$.

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