
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. 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 it is empty.

b) Suppose that if a pair is mixed-color, it is set aside, while if the pair is same-color, it is returned to the box. This operation is called an attempt. Find the expected number of attempts needed to set all the balls aside, so that nothing remains in the box.

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