
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 participate in a soccer tournament where each team plays every other team exactly once. No ties are allowed, each team has a 50% chance of winning any game, and game outcomes are independent. Each game win awards the winner one point and the loser zero points. The total points determine the final rankings. In the first games of the tournament, team \(A\) beats team \(C\) and team \(B\) beats team \(D.\) Find the probability that team \(A\) finishes with more points than team \(B\), expressed as a fraction \(m/n\) where \(m\) and \(n\) are relatively prime. Find \(m+n.\)

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