
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
Pyotr Ivanovich, along with 49 other men and 50 women, sit in random order around a circular table.

Let's define a man as satisfied if there is a woman sitting next to him. Find:

a) the probability that Pyotr Ivanovich is satisfied;

b) the expected number of satisfied men.

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