
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 the World Series of baseball, the Astros are playing against the Dodgers. To win the World Series, a team must win 4 games before the other team does. If the Dodgers win each game with a probability of $\dfrac{3}{4}$ and there are no ties, what is the probability that the Astros will win the World Series but that the contest will need all seven games to be decided?

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