
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 an extended game of 8 rounds, where Alex, Mel, and Chelsea participate in each round as before, the probability of Alex winning a round remains $\frac{1}{2}$, while Mel's chance of winning any round is twice that of Chelsea's. If the outcomes of the rounds are independent, what is the probability that Alex wins 4 rounds, Mel wins 3 rounds, and Chelsea wins 1 round?
- **A** $\frac{35}{324}$
- **B** $\frac{1}{12}$
- **C** $\frac{20}{243}$
- **D** $\frac{70}{729}$
- **E** $\frac{5}{162}$

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