
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
Four points are chosen uniformly at random on a circle. What is the probability that no two of these points form an obtuse triangle with the circle's center, when considering triangles formed by the center and any two of the four points?

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