
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 8-round game where Alex, Mel, and Chelsea each have chances to win independently in each round. Alex has a probability of $\frac{1}{2}$ of winning each round. Mel is three times more likely to win any round than Chelsea. Calculate the probability that Alex wins four rounds, Mel wins three rounds, and Chelsea wins one round.
A) $\frac{945}{8192}$  
B) $\frac{27}{512}$  
C) $\frac{1}{16}$  
D) $\frac{1}{8}$  
E) $\frac{1}{15}$

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