A square has sides of length $10$, and a circle centered at one of its vertices has radius $10$. What is the area of the union of the regions enclosed by the square and the circle? Express your answer in the form \(a + b\pi\), where \(a\) and \(b\) are integers. Please give the value of \(a + b\).

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