
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 certain World Cup, the Brazil team's probabilities of outcomes against each opponent are as follows:  
- Winning: $\frac{1}{2}$  
- Drawing: $\frac{1}{3}$  
- Losing: $\frac{1}{6}$  

Points awarded are:  
- Win: 3 points  
- Draw: 1 point  
- Loss: 0 points  

During the group stage, each team plays three matches, and a team needs to earn at least 4 points to advance to the knockout stage. In the knockout stage, if a match ends in a draw, it goes to a penalty shootout. The probability of Brazil winning a penalty shootout is $\frac{3}{5}$. What is the probability that Brazil wins the championship with exactly one of the four knockout stage matches decided by a penalty shootout?

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