
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]


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In an acute triangle △ABC, the sides opposite to the internal angles A, B, C are denoted as a, b, c respectively, and $$1+ \frac{\sqrt{3}}{3}\sin{2A} = 2\sin^2{\frac{B+C}{2}}$$.
(I) Determine angle A;
(II) If the radius of the circumcircle of △ABC is $$2\sqrt{3}$$, find the maximum area of triangle ABC.

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