
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 $\overrightarrow{a}=(\cos α,\sin α)$ and $\overrightarrow{b}=(\cos β,\sin β)\left(-\frac{π}{2} < α < 0,0 < β < \frac{π}{2}\right)$, and $|\overrightarrow{a}-\overrightarrow{b}|=\frac{\sqrt{10}}{5}$.
1) Find the value of $\cos (α-β)$;
2) If $\cos α=\frac{12}{13}$, find the value of $\cos β$.

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