
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 6. If $AB$ and $CD$ are perpendicular, and the shaded region consists of triangle $AOB$ and sector $COD$, where $O$ is the center of the circle and $\angle COD = 45^\circ$, what is the area of the shaded region?
[asy]
size(120);
import graph;
fill((0,0)--(1,-1)--cycle,mediumgray);
fill(Arc((0,0),sqrt(2),270,315)--cycle,mediumgray);
draw(Circle((0,0),sqrt(2)));
draw((-1,-1)--(1,1)--(1,-1)--(-1,1)--cycle);
label("$A$",(-1,1),NW); label("$C$",(1,1),NE); label("$D$",(-1,-1),SW); label("$B$",(1,-1),SE);

[/asy]

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