
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 an acute triangle $△ABC$ with angles $A$, $B$, $C$ and their respective opposite sides $a$, $b$, $c$, define vectors $\overrightarrow{m}=(2\sin B, \sqrt {3})$ and $\overrightarrow{n}=(2\cos ^{2} \frac {B}{2}-1,\cos 2B)$, where $\overrightarrow{m} \perp \overrightarrow{n}$.

1. Determine the size of angle $B$.
2. Find the monotonically increasing interval of the function $f(x)=\sin 2x\cos B-\cos 2x\sin B$.
3. If $b=4$, find the range of values for the area of $△ABC$.

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