
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
It is known that points $S$, $A$, $B$, and $C$ lie on the surface of a sphere $O$, with $SA \perpendicular$ plane $ABC$, $AB \perpendicular BC$, $SA=AB=1$, and $BC= \sqrt{2}$. Find the surface area of sphere $O$.

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