
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 \( a \), \( b \), and \( c \) respectively, and it is given that \( \dfrac{b\cos C + c\cos B}{2} = \dfrac{\sqrt{3}}{3}a\cos B \).  
\( (1) \) Find \( B \);  
\( (2) \) If \( b = \sqrt{7} \), \( c = 2\sqrt{3} \), and \( a > b \), calculate the area of \( \triangle ABC \).

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