
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 $\overrightarrow{a}=(\cos \alpha,\sin \alpha)$, $\overrightarrow{b}=(\cos \beta,\sin \beta)$, $(0 < \beta < \alpha < \pi)$.  
$(1)$ If $|\overrightarrow{a}- \overrightarrow{b}|= \sqrt {2}$, find the angle $\theta$ between $\overrightarrow{a}$ and $\overrightarrow{b}$;  
$(2)$ Let $\overrightarrow{c}=(0,1)$. If $\overrightarrow{a}+ \overrightarrow{b}= \overrightarrow{c}$, find the values of $\alpha$ and $\beta$.

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