
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 the vectors $\overset{→}{m}=(2,\sin α)$, $\overset{→}{n}=(\cos α,-1)$, where $α∈(0,π2)$, and $\overset{→}{m}⊥\overset{→}{n}$.
(1) Find the values of $\sin 2α$ and $\cos 2α$;
(2) If $\sin(α−β)=\dfrac{\sqrt{10}}{10}$, and $β∈(0,\dfrac{π}{2})$, find the angle $β$.

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