
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 a diagram, diameters $AB$ and $CD$ of a circle are perpendicular to each other and intersect at the circle's center $O$. If the radius of the circle is 6, calculate the area of the shaded region created by sectors $AOB$ and $COD$, along with triangles $AOC$ and $BOD$.

[asy]
size(120);
import graph;
fill((-1.8,-1.8)--(-1.8,1.8)--(1.8,1.8)--(1.8,-1.8)--cycle,mediumgray);
fill(Arc((0,0),sqrt(18),45,135)--cycle,mediumgray);fill(Arc((0,0),sqrt(18),225,315)--cycle,mediumgray);
draw(Circle((0,0),sqrt(18)));
draw((-1.8,-1.8)--(1.8,1.8)--(1.8,-1.8)--(-1.8,1.8)--cycle);
label("$A$",(-1.8,1.8),NW); label("$C$",(1.8,1.8),NE); label("$D$",(-1.8,-1.8),SW); label("$B$",(1.8,-1.8),SE);
[/asy]

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