
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
In a square grid where each square has a side length of $10 \mathrm{~cm}$, a circle is drawn with center $S$ at a marked lattice point and radius $20 \mathrm{~cm}$.

Points $A, B, C$, and $D$ are the intersections of the circle with the grid lines.

Determine the area of the shaded region $A B C D$.

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