
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 cup tournament system to determine the winner among 8 athletes involves pairing up players through a draw. Four matches determine four winners who participate in the second round; the third round is the final. The winner of the final match gets the first prize, and their opponent gets the second prize. Assume each player has a certain strength (similar to how each object has a certain weight) and that a stronger player always wins against a weaker one (similar to how a heavier object always outweighs a lighter one if placed on different sides of a scale). Under these assumptions, the described process is appropriate for determining the champion since the winner will indeed be stronger than all their opponents; however, the second place will not always be occupied by the second strongest player.

What is the probability that the runner-up in the final match truly deserves the second prize?

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