
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 of two concentric circles is divided into two equal areas, and $O$ is the center of both circles. The area of the outer circle is $100\pi$. What is the total area of the shaded regions? [asy]
size(100);
import graph;
fill(Arc((0,0),5,180,360)--cycle,mediumgray);fill(Arc((0,0),2.5,0,180)--cycle,mediumgray);
draw(Circle((0,0),5));
draw(Circle((0,0),2.5));

dot((0,0)); label("$O$",(0,0),N);
draw((-5,0)--(5,0)); draw((-2.5,0)--(2.5,0));
[/asy]

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