
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, $AB$ and $CD$ are diameters of a circle with radius 5. If $AB$ and $CD$ are perpendicular, what is the area of the shaded region?

[asy]
size(120);
import graph;
fill((-1.25,-1.25)--(-1.25,1.25)--(1.25,1.25)--(1.25,-1.25)--cycle,mediumgray);
fill(Arc((0,0),sqrt(2.5),45,135)--cycle,mediumgray);fill(Arc((0,0),sqrt(2.5),225,315)--cycle,mediumgray);
draw(Circle((0,0),sqrt(2.5)));
draw((-1.25,-1.25)--(1.25,1.25)--(1.25,-1.25)--(-1.25,1.25)--cycle);
label("$A$",(-1.25,1.25),NW); label("$C$",(1.25,1.25),NE); label("$D$",(-1.25,-1.25),SW); label("$B$",(1.25,-1.25),SE);
[/asy]

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