For her daughter's $12^{\text{th}}$ birthday, Ingrid decides to bake a dodecagon pie in celebration. Unfortunately, the store does not sell dodecagon-shaped pie pans, so Ingrid bakes a circular pie first and then trims off the sides in a way such that she gets the largest regular dodecagon possible. If the original pie was $8$ inches in diameter, the area of pie that she has to trim off can be represented in square inches as $a\pi - b$ where $a, b$ are integers. What is $a + b$?

Let's think step by step and output the final answer within \boxed{}.
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