
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
Noble maidens went to the theater. There are $n$ maidens in total, and they all have tickets for a single row with exactly $n$ seats. If a maiden needs to pass by an already seated maiden to reach her seat, the seated maiden must stand up politely to let her friend pass.

a) (8th grade, 2 points). Find the expected number of times maidens will stand up.

b) (9th grade, 5 points). Find the expected number of maidens who will not have to stand up at all.

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