
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 sphere $O$, where $SA\bot $ plane $ABC$, $AB\bot BC$, $SA=AB=1$, and $BC=\sqrt{2}$, the surface area of sphere $O$ is ____.

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