
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
Three candidates, A, B, and C, are vying for a single spot to participate in a national speech. The winner will be determined by a lottery. Two black balls and one red ball are placed in a bag. The candidates will draw balls in the order of A, B, and C. The one who draws the red ball will win the spot.

1) What is the probability that B draws the red ball given that A has drawn a black ball?
2) If A draws first and gets the red ball, is this fair to candidates B and C?

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