
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 a triangle \( \triangle ABC \) where the sides opposite to angles \( A \), \( B \), and \( C \) are \( a \), \( b \), and \( c \) respectively, and the circumradius \( R = \sqrt{3} \), satisfying the condition \( \tan B + \tan C = \frac{2 \sin A}{\cos C} \):
(1) Find the measures of angle \( B \) and side \( b \);
(2) Find the maximum area of \( \triangle ABC \).

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