
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 girls went to the theater. There are a total of \( n \) girls, and they all have tickets for one row which has exactly \( n \) seats. If a girl needs to pass by a girl who is already seated to reach her own seat, the seated girl must politely stand up to let her friend pass.

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

b) (9th grade. 5 points). Find the expected number of people who will never have to stand up.

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