
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
Alex, Mel, and Chelsea play a game consisting of 8 rounds where each round has a single winner, and the rounds are independent. The probability Alex wins a round is $\frac{1}{3}$, and Mel is three times as likely to win as Chelsea. Find the probability that Alex wins 4 rounds, Mel wins 3 rounds, and Chelsea wins 1 round.
A) $\frac{35}{486}$
B) $\frac{1}{280}$
C) $\frac{70}{972}$
D) $\frac{1}{432}$
E) $\frac{5}{36}$

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