
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 two equal halves, 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 when the smaller circle's diameter equals half the radius of the larger circle? 
[asy]
size(100);
import graph;
fill(Arc((0,0),3,180,360)--cycle,mediumgray);fill(Arc((0,1.5),1.5,0,180)--cycle,mediumgray);
draw(Circle((0,0),3));
draw(Circle((0,1.5),1.5));

dot((0,0)); label("$O$",(0,0),N);
draw((-3,0)--(3,0)); draw((-1.5,1.5)--(1.5,1.5));
[/asy]

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