
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 version of the game, Alex, Mel, and Chelsea play 7 rounds. In each round, there is a single winner, and the outcomes of the rounds are independent. The probability that Alex wins any round is $\frac{3}{5}$. Mel is still twice as likely to win as Chelsea. What is the probability that Alex wins four rounds, Mel wins two rounds, and Chelsea wins one round?

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