
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 with diagonal length $2$ and a circle of radius $1$ share the same center. What is the area inside the circle, but outside the square?
A) $\pi - 1$
B) $\pi - 2$
C) $2\pi - 4$
D) $\pi + 2$

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