
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 the radius of sphere $O$ is 2, and circle $O_1$ is a smaller circle with $O_{1}O= \sqrt {2}$. Points $A$ and $B$ are on circle $O_1$, and if $\angle AO_{1}B= \frac {\pi }{2}$, then the spherical distance between points $A$ and $B$ is __________.

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