
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, $PQ$ is a diameter of a circle with radius 5, and $OR$ and $OS$ are radii perpendicular to each other and to $PQ$. If $R$ and $S$ are points on the circle such that $\angle ROS = 90^\circ$, what is the area of the shaded region?

[asy]
size(140);
import graph;
fill((-2.5,0)--(0,2.5)--(0,-2.5)--cycle,mediumgray);
fill(Arc((0,0), sqrt(4.5),30,120)--cycle,mediumgray);
draw(Circle((0,0), 5));
draw((-5,0)--(5,0));
draw((0,0)--(0,5));
draw((0,0)--(0,-5));
label("$P$",(-5,0),W); label("$Q$",(5,0),E); label("$R$",(0,5),N); label("$S$",(0,-5),S); label("$O$",(0,0),SE);
[/asy]

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