
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
Monty wishes to secure his cat with a 15-foot leash to an octagonal playhouse that is 10 feet on each side. Monty is comparing two different tying points for the leash:
- In arrangement I, the cat is tied to the midpoint of one side of the octagon.
- In arrangement II, the cat is tied 5 feet away from a corner of the octagon.
Determine which of these arrangements give the cat the greater area to roam and by how many square feet.
A) I, by 62.5π
B) I, by 52.5π
C) II, by 52.5π
D) II, by 62.5π
E) II, by 72.5π

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