
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, the larger circle is divided into four equal sectors and the smaller circle into two equal halves. $O$ 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),3,0,90)--cycle,mediumgray);
fill(Arc((0,0),3,180,270)--cycle,mediumgray);
fill(Arc((0,1.5),1.5,90,270)--cycle,mediumgray);
draw(Circle((0,0),3));
draw(Circle((0,1.5),1.5));

dot((0,0)); label("$O$",(0,0),N);
[/asy]

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