
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 $\triangle ABC$ with internal angles $A$, $B$, $C$ and their corresponding opposite sides $a$, $b$, $c$. $B$ is an acute angle. Vector $m=(2\sin B, -\sqrt{3})$ and vector $n=(\cos 2B, 2\cos^2 \frac{B}{2} - 1)$ are parallel.

(1) Find the value of 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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