
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
A rectangle has dimensions of 8 by 12, and a circle centered at one of its vertices has a radius of 8. What is the area of the union of the regions enclosed by the rectangle and the circle? Express your answer in terms of \(\pi\).

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