
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 the triangular pyramid \( S-ABC \) with a base \( ABC \) that is an isosceles right triangle with \( AB \) as the hypotenuse. It holds that \( SA = SB = SC = 2 \) and \( AB = 2 \). If points \( S \), \( A \), \( B \), and \( C \) all lie on the surface of a sphere centered at point \( O \), find the distance from point \( O \) to the plane \( ABC \).

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