
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 \( p \) pairs of socks hanging out to dry in a random order (as they were taken out of the washing machine). There are no identical pairs of socks. The socks hang behind a drying sheet, so the Absent-Minded Scientist reaches out and takes one sock at a time by touch, comparing each new sock with all previous ones. Find the expected value of the number of socks taken by the Scientist until he gets any pair.

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