
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 that involves 8 rounds. In each round, only one of them wins, and the outcomes of the rounds are independent. Each round, the probability of Alex winning is $\frac{1}{2}$. Mel and Chelsea have equal probabilities of winning any round. Calculate the probability that Alex wins four rounds, Mel wins three rounds, and Chelsea wins one round.

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