
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 furiously cuts a rectangular sheet of paper with scissors. Every second, he makes a straight random cut on the first piece he encounters, dividing it into two parts.

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

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

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