
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 respective opposite sides $a$, $b$, $c$. $B$ is an acute angle. The vectors $\overset{→}{m}=\left(2\sin B,-\sqrt{3}\right)$, $\overset{→}{n}=\left(\cos 2B,2\cos^2 \frac{B}{2}-1\right)$ are parallel.

(1) Find the measure of angle $B$;

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

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