
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
Eight teams play a soccer tournament where each team again plays every other team exactly once. Each game results in a win or a loss, with no ties, and every team has an equal chance of winning. The first game between team $A$ and team $B$ results in team $B$ defeating team $A$. What is the probability that team $B$ finishes with more points than team $A$ at the end of the tournament? Express your answer as a fraction $m/n$, where $m$ and $n$ are relatively prime positive integers.

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