
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 $S$, $A$, $B$, $C$ on the surface of a sphere $O$, $SA \perp$ plane $ABC$, $AB \perp BC$, $SA = AB = 1$, $BC = \sqrt{2}$, calculate the surface area of sphere $O$.

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