
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
The probability of successfully completing the exercise for each of the two athletes is 0.5. The athletes perform the exercise in turns, with each making two attempts. The one who completes the exercise first wins the prize. Find the probability of each athlete winning the prize.

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