
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
André, Bianca, Carlos, and Dalva want to raffle a book among themselves. To do this, they place 3 white balls and 1 black ball in a box and agree that, in alphabetical order of their names, each of them will draw a ball, without returning it to the box. Whoever draws the black ball will win the book.

a) What is the probability that André wins the book?

b) What is the probability that Dalva wins the book?

To raffle another book among them, André suggested using 2 black balls and 6 white balls. As before, the first person to draw a black ball will win the book; if the first four balls drawn are white, they will continue to draw balls in the same order. In this new raffle:

c) What is the probability that André wins the book?

d) What is the probability that Dalva wins the book?

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