
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 championship participated by three players: A, B, and C, the matches are conducted according to the following rules: the first match is between A and B; the second match is between the winner of the first match and C; the third match is between the winner of the second match and the loser of the first match; the fourth match is between the winner of the third match and the loser of the second match. Based on past records, the probability of A winning over B is 0.4, B winning over C is 0.5, and C winning over A is 0.6.  
(1) Calculate the probability of B winning four consecutive matches to end the competition;  
(2) Calculate the probability of C winning three consecutive matches to end the competition.

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