
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

There are $n$ white and $n$ black balls in a box. The balls are drawn from the box two at a time, forming random pairs.

a) Find the expected number of mixed-color pairs drawn from the box by the time the box is empty.

b) Assume that if a pair is mixed-color, it is set aside, while same-color pairs are returned to the box. This operation is called an attempt. Find the expected number of attempts needed for all the balls to be set aside and the box to be empty.

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