
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
Nine teams play a soccer tournament where each team plays every other team exactly once. There are no ties allowed; each match has a winner and a loser, with each team having a 50% chance of winning any match. In each match, the winner scores a point. After all matches, total points determine team rankings. In the first match of the tournament, Team $A$ beats Team $B$. Calculate the probability that after all matches, Team $A$ finishes with more points than Team $B$. Express your answer as a fraction $m/n$, where $m$ and $n$ are relatively prime positive integers, and find $m+n$.

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