
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
Roger wishes to secure his dog with a 10-foot rope to a rectangular shed that is 20 feet long and 12 feet wide. He ties the dog to a point halfway along the longer side of the shed. He is considering two arrangements:
1. Tying the dog directly at the middle of the long side.
2. Tying the dog 5 feet away from the middle towards one end of the shed.
Which of these arrangements gives the dog the greater area to roam, and by how many square feet?
A) Arrangement 1, by 25π square feet
B) Arrangement 2, by 25π square feet
C) Arrangement 1, by 75π square feet
D) Arrangement 2, by 50π square feet

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