
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 straight cut through a random piece, splitting it into two parts.

a) Find the expected number of sides of the polygon that Vasya randomly picks after an hour of this activity.

b) Solve the 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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