
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 to angles A, B, and C respectively in triangle ABC, and they satisfy the equation $(b + c - a)(\sin A + \sin B + \sin C) = c \sin B$.

1. Find the measure of angle A.
2. Given that $a = 2\sqrt{3}$, and $S$ is the area of triangle ABC, find the maximum value of $S + 4\sqrt{3} \cos B \cos C$.

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