
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 $\overrightarrow{a}=(\sin \alpha, -2)$, $\overrightarrow{b}=(1, \cos \alpha)$, and $\overrightarrow{a}⊥\overrightarrow{b}$.  
$(1)$ Find the value of $\cos^2\alpha - \sin \alpha \cos \alpha$;  
$(2)$ If $α∈(0,\frac{π}{2})$, $β∈(-\frac{π}{2},0)$, and $\cos(α-β)=-\frac{{\sqrt{10}}}{10}$, find the value of $\beta$.

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