
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 game played over 8 rounds, Alex, Mel, and Chelsea compete where each round has one winner, and the probabilities for winning are not evenly distributed. Alex has a probability $\frac{1}{4}$ of winning each round, Mel is twice as likely to win as Chelsea. What is the probability that Alex wins 2 rounds, Mel wins 3 rounds, and Chelsea wins 3 rounds?
A) $\frac{15}{512}$
B) $\frac{21}{512}$
C) $\frac{28}{512}$
D) $\frac{35}{512}$
E) $\frac{42}{512}$

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