
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
Po picks  $100$  points  $P_1,P_2,\cdots, P_{100}$  on a circle independently and uniformly at random. He then draws the line segments connecting  $P_1P_2,P_2P_3,\ldots,P_{100}P_1.$  Find the expected number of regions that have all sides bounded by straight lines.

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