
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 plays every other team exactly once. There are no ties and each team has a $50\%$ chance of winning any given game, with each outcome independent of the others. Winners receive one point and losers receive zero points, with the total points used to determine rankings. In the first game of the tournament, team $A$ loses to team $B$. The probability that team $A$ finishes with more points than team $B$ is $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

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