
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
Given Alex, Jamie, and Casey play a game over 8 rounds, and for each round, the probability Alex wins is $\frac{1}{3}$, and Jamie is three times as likely to win as Casey, calculate the probability that Alex wins four rounds, Jamie wins three rounds, and Casey wins one round.

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