
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
Given a circle with center $O$ and radius 7, radii $OP$ and $OQ$ form a 120-degree angle at $O$. Calculate the perimeter of the shaded region that includes the arc $PQ$ and segments $OP$ and $OQ$.

[asy]
size(100);
import graph;
label("$P$",(-0.7,-0.7),W); label("$O$",(0,0),NE); label("$Q$",(0.7,-0.7),E);

fill(Arc((0,0),1,-60,180)--cycle,mediumgray);
draw(Arc((0,0),1,-60,180));
fill((0,0)--(-0.7,-0.7)--(0.7,-0.7)--cycle,white);
draw((-0.7,-0.7)--(0,0)--(0.7,-0.7));
draw((-.1,-0.7)--(-.1,-0.8)--(0,-0.8));

[/asy]

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