
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 vectors $\overrightarrow{m}=(\cos α,-1)$ and $\overrightarrow{n}=(2,\sin α)$, where $α∈(0, \dfrac {π}{2})$, and $\overrightarrow{m}⊥ \overrightarrow{n}$.
(1) Find the value of $\cos 2α$;
(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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