
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 to the internal angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$, respectively. Given the vectors $\overrightarrow{m}=(2\sin B,-\sqrt{3})$ and $\overrightarrow{n}=(\cos 2B,2\cos^2 \frac{B}{2}-1)$ with $\overrightarrow{m} \parallel \overrightarrow{n}$:
(I) Find the magnitude of the acute angle $B$;
(II) If $b=2$, find the maximum value of the area $S_{\triangle ABC}$ of the triangle $ABC$.

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