
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 modified game with $7$ rounds, the outcomes of the rounds are still independent. The probability that Alex wins each round remains the same at $\frac{1}{2}$, while Mel is now thrice as likely to win as Chelsea. Determine the probability that Alex wins four rounds, Mel wins two rounds, and Chelsea wins one round.
A) $\frac{35}{256}$
B) $\frac{63}{512}$
C) $\frac{945}{8192}$
D) $\frac{15}{1024}$

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