
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
Peter Ivanovich, 49 other men, and 50 women are seated in a random order around a circular table. We call a man "satisfied" if there is a woman sitting next to him. Find:

a) the probability that Peter Ivanovich is satisfied;

b) the expected number of satisfied men.

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