
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 $\overrightarrow{a}=(2\cos α,2\sin α), \overrightarrow{b}=(\cos β,\sin β)$, $0 < α < β < 2π$.
(I) If $\overrightarrow{a} \perp \overrightarrow{b}$, find the value of $| \overrightarrow{a}-2 \overrightarrow{b}|$;
(II) Let $\overrightarrow{c}=(2,0)$, if $\overrightarrow{a}+2 \overrightarrow{b}= \overrightarrow{c}$, find the values of $α$, $β$.

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