
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 \( \triangle ABC \), the sides opposite to angles \( A \), \( B \), and \( C \) are denoted as \( a \), \( b \), and \( c \) respectively, with vectors \( \boldsymbol{m} = (2 \sin B, -\sqrt{3}) \) and \( \boldsymbol{n} = \left(\cos 2B, 2 \cos^2 \frac{B}{2} - 1\right) \), and \( \boldsymbol{m} \parallel \boldsymbol{n} \).

(1) Find the measure of the acute angle \( B \).

(2) If \( b = 2 \), find the maximum value of the area \( S_{\triangle ABC} \).

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