
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
Vasya is furiously cutting a rectangular piece of paper with scissors. Every second he cuts the first piece he sees with a random straight cut into two parts.

a) Find the expected number of sides of the polygon that Vasya will randomly encounter after an hour of such work.

b) Solve the same problem if the initial paper had the shape of an arbitrary polygon.

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