
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
Six teams play in a soccer tournament where each team faces every other team exactly once. Each match results in a win or a loss, with no ties allowed. Winners receive one point; losers receive none. In the first match, Team $A$ defeats Team $B$. Assuming each team has an equal chance to win each match, and all match outcomes are independent, find the probability that Team $A$ scores more points than Team $B$ throughout the tournament. Let this probability be expressed as a fraction $m/n$ in its simplest form. Find $m+n$.

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