
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 $α \in (0, \dfrac{π}{2} )$, and $\overrightarrow{m} \perp \overrightarrow{n}$.

(1) Find the value of $\cos 2α$.

(2) If $\sin \left(α-β\right)= \dfrac{ \sqrt{10}}{10}$, and $β \in (0, \dfrac{π}{2} )$, find the value of angle $β$.

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