
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, $O$ is the center of a circle with radii $OP=OQ=7$. What is the perimeter of the shaded region?

[asy]
size(100);
import graph;
label("$P$", (1,0), E); label("$O$", (0,0), NE); label("$Q$", (0,1), N);

fill(Arc((0,0),1,0,270)--cycle,mediumgray);
draw(Arc((0,0),1,0,270));
fill((0,0)--(1,0)--(0,1)--cycle,white);
draw((1,0)--(0,0)--(0,1));
draw((.1,0)--(.1,.1)--(0,.1));

[/asy]
In this diagram, $P$ and $Q$ are points on the circumference of the circle such that the arc $PQ$ spans \(270^\circ\). Calculate the perimeter of the shaded region.

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