
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 sheet of paper with scissors. Every second, he makes a random straight cut on the first available piece, splitting it into two parts.

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

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

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