
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 the diagram, each circle is divided into four equal areas and $O$ is the center of the larger circle. The area of the larger circle is $100\pi.$ What is the total area of the shaded regions? [asy]
size(100);
import graph;
fill(Arc((0,0),2,90,270)--cycle,mediumgray);fill(Arc((0,1),1,270,450)--cycle,mediumgray);
draw(Circle((0,0),2));
draw(Circle((0,1),1));

dot((0,0)); label("$O$",(0,0),N);
draw((-2,0)--(2,0)); draw((-1,1)--(1,1));
[/asy]

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