
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

On a drying rack, $n$ socks are hanging in a random order (as they were taken out of the washing machine). Among them are two of Absent-Minded Scientist's favorite socks. The socks are hidden by a drying sheet, so the Scientist cannot see them and picks one sock at a time by feel. Find the expected number of socks the Scientist will have taken by the time he has both of his favorite socks.

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