
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 $0＜α＜\frac{π}{2}$, $-\frac{π}{2}＜β＜0$, $cosα=\frac{\sqrt{2}}{10}$, $sinβ=-\frac{\sqrt{5}}{5}$. Find:<br/>
$(1)$ The value of $\cos \left(\alpha -\beta \right)$;<br/>
$(2)$ The value of $\alpha -2\beta$.

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