
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
Nine teams participate in a basketball tournament with each team playing every other team exactly once. Each match results in a win or a loss with no ties, and every team has a 50% chance of winning any given game. Winners get 1 point and losers get none. The first game of the tournament sees team $A$ defeating team $B$ and team $C$ defeating team $D.$ Calculate the probability that team $A$ ends up with more points than both team $B$ and team $C$ combined, expressed as a simplified fraction $m/n$. What is $m+n$?

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