
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 that $a$, $b$, and $c$ are the sides opposite angles $A$, $B$, and $C$ of $\triangle ABC$ respectively, consider the function $$f(x) = 3 + 2 \sqrt{3} \sin x \cos x + 2 \cos^2 x$$ and $f(A) = 5$,
(1) Find the magnitude of angle $A$.
(2) If $a = 2$, find the maximum possible area of $\triangle ABC$.

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