
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 that $π < α < 2π$, vectors $ \overrightarrow{a}=(-2,1)$, $ \overrightarrow{b}=(\sin α,2\cos α)$, $ \overrightarrow{c}=(\cos α,-2\sin α)$.
(1) If $ \overrightarrow{a}⊥ \overrightarrow{b}$, find $α$;
(2) If $| \overrightarrow{b}+ \overrightarrow{c}|= \sqrt {3}$, find the value of $\sin α+\cos α$.

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