
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
Six points are chosen uniformly, but at three distinct equidistant arcs along a circle. What is the probability that any triangle formed by choosing any three points out of these six does not contain an obtuse angle with the circle's center as one of its vertices?

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