
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 $\overrightarrow{a}=(\cos α,\sin α)$ and $\overrightarrow{b}=(\cos β,\sin β)$ with $| \overrightarrow{a}- \overrightarrow{b}|= \frac {2}{5} \sqrt {5}$,

1. Find the value of $\cos (α-β)$
2. If $- \frac {π}{2} < β < 0 < α < \frac {π}{2}$ and $\sin β=- \frac {5}{13}$, find the value of $\sin α$.

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