
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
A running competition on an unpredictable distance is conducted as follows. On a round track, two points \( A \) and \( B \) are chosen randomly (with the help of a spinning arrow), after which the athletes run from \( A \) to \( B \) along the shorter arc. A spectator bought a ticket to the stadium and wants the athletes to run past their seat (so they can take a good photograph). What is the probability that this will happen?

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