
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
Five basketball teams participate in a round-robin tournament where each team plays every other team exactly once. Each game results in either a win or a loss with no ties, and each team has a $50\%$ chance of winning any game against any opponent, with outcomes being independent. In each game, the winner earns a point while the loser earns none. The first game results in team $A$ defeating team $B$. Compute the probability that at the end of the tournament, team $A$ finishes with more points than team $B$. Express your answer as a fraction $m/n$, where $m$ and $n$ are coprime integers. Find $m+n$.

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