
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
In triangle $ABC$, let $a$, $b$, $c$ be the lengths of the sides opposite to angles $A$, $B$, and $C$, respectively. Given the vectors $\overrightarrow{m} = (a, b+c)$ and $\overrightarrow{n} = (1, \cos C + \sqrt{3}\sin C)$, and $\overrightarrow{m}$ is parallel to $\overrightarrow{n}$.  
(1) Find angle A.  
(2) If $3bc = 16 - a^2$, determine the maximum area of triangle $ABC$.

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