
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. No ties occur, each match winner earns a point, losers get 0, and every game's outcome is independent with a $50\%$ chance of winning for either team. If team $A$ wins against team $B$ in their first game, what is the probability that team $A$ finishes with more total points than team $B$?

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