
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 points $A(2,0)$, $B(0,2)$, and $C(\cos α,\sin α)$ where $0 < α < π$,
1. If $| \overrightarrow{OA}+ \overrightarrow{OC}|= \sqrt {7}$, find the angle between $ \overrightarrow{OB}$ and $ \overrightarrow{OC}$;
2. If $ \overrightarrow{AC}⊥ \overrightarrow{BC}$, find the value of $\cos α$.

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