
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 $ABC$, the sides opposite angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$ respectively, and it is given that $2\sin A \cos B + \sin B = 2\sin C$.
(1) Determine angle $A$;
(2) If $a = 4\sqrt{3}$ and $b + c = 8$, find the area of triangle $ABC$.

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