
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
In a soccer tournament, six teams play against each other, each team competing exactly once with every other team. Each game results either in a win or a loss, with no draws allowed, and each win garners 1 point. Suppose that in the first two games of the tournament, team $A$ beats team $B$, and in the next game, team $A$ also beats team $C$. Calculate the probability that, by the end of the tournament, team $A$ finishes with more points than both team $B$ and team $C$. Assume each team has an equal probability of winning any given match and that the outcomes of different games are independent.

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