
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
Seven teams participate in a soccer tournament where each team plays every other team once. Team $A$ has a 60% chance to win the first game against Team $B$, after which each game (including those involving Teams $A$ and $B$ but not against each other) has independent outcomes with each team having a 50% chance to win. If a team wins a match, it is awarded a point, and the loser receives none. After the first match where Team $A$ faces Team $B$, calculate the probability that Team $A$ ends up with more points than Team $B$. Express your answer as a fraction in its lowest terms and find $m+n$, where $m/n$ is the fraction.

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