
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 $n$ girls in total, and they all have tickets for one row with exactly $n$ chairs. If a girl needs to pass by another girl already seated to reach her place, the latter must politely stand up to let her friend pass.

a) Find the expected number of times girls will need to stand up.

b) Find the expected number of girls who never have to stand up even once.

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