
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 a total of $n$ maidens, and each has a ticket for a row with exactly $n$ seats. If a maiden needs to pass an already seated maiden to reach her seat, the seated one must politely stand to let her friend pass.

a) Find the expected number of times maidens will have to stand.

b) Find the expected number of maidens who will not have to stand at all.

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