
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, $PQ$ and $RS$ are diameters of a circle with radius 6. Diameter $RS$ is rotated to be at a 45-degree angle to diameter $PQ$, which remains horizontal. What is the area of the shaded region formed by the quadrants and triangles created by these diameters?

[asy]
size(120);
import graph;
fill((-1.5,-1.5)--(-1.5,1.5)--(1.5,1.5)--(1.5,-1.5)--cycle,mediumgray);
fill(Arc((0,0),3*sqrt(2)/2,45,135)--cycle,mediumgray);fill(Arc((0,0),3*sqrt(2)/2,225,315)--cycle,mediumgray);
draw(Circle((0,0),3*sqrt(2)/2));
draw((-1.5,-1.5)--(1.5,1.5)--(1.5,-1.5)--(-1.5,1.5)--cycle);
label("$P$",(-1.5,1.5),NW); label("$R$",(1.5,1.5),NE); label("$S$",(-1.5,-1.5),SW); label("$Q$",(1.5,-1.5),SE);
[/asy]

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