
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
Jane wishes to secure her rabbit using a 10-foot rope to a rectangular hutch that measures 20 feet by 10 feet. She can connect the rope either to the midpoint of one of the longer sides or to a point 3 feet from the corner along the shorter side. 

Which rope tying points provide the rabbit the larger area to roam in, and by how many square feet?
A) Midpoint of long side, by 22.75π square feet
B) 3 feet from corner on short side, by 22.75π square feet
C) Midpoint of long side, by 50π square feet
D) 3 feet from corner on short side, by 72.75π square feet

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