
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 box, there are $n$ white and $n$ black balls. Balls are drawn from the box two at a time - randomly paired.

a) Find the expected number of pairs of different colors drawn from the box by the time the box is empty.

b) Suppose that if a pair is of different colors, it is set aside, and if it is of the same color, it is returned to the box. This operation is called an attempt. Find the expected number of attempts needed for all balls to be set aside, leaving the box empty.

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