
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 square is inscribed in a circle of radius  $6$ . A quarter circle is inscribed in the square, as shown in the diagram below. Given the area of the region inside the circle but outside the quarter circle is  $n\pi$  for some positive integer  $n$ , what is  $n$ ?
[asy]
        size(5 cm);
        draw((0,0)--(2,0)--(2,2)--(0,2)--cycle);
        draw(circle((1,1),1.41));
        draw(arc((0,0),2,0,90));[/asy]


*2021 CCA Math Bonanza Lightning Round #1.2*

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