
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 Go game competition involving three players, the probability of player A beating player B is 0.4, the probability of player B beating player C is 0.5, and the probability of player C beating player A is 0.6. The competition proceeds according to the following rules:  
First round: A vs B;  
Second round: Winner of the first round vs C;  
Third round: Winner of the second round vs Loser of the first round;  
Fourth round: Winner of the third round vs Loser of the second round.  
Calculate:  
(1) The probability of player B winning four consecutive rounds;  
(2) The probability of player C winning three consecutive rounds.

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