
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
The point $P$ is the center of a circle that circumscribes triangle $XYZ$, where $\angle XPY = 150^\circ$ and $\angle XPZ = 110^\circ$. Determine the degree measure of $\angle XYZ$.

[asy]
pair X,Y,Z;
draw(Circle((0,0),20),linewidth(0.7));
label("$P$",(0,0),S);
X=(-16,-12);
Z=(16,-12);
Y=(3,19.7);
draw(X--Y--Z--cycle,linewidth(0.7));
label("$110^\circ$",(-0.2,-0.3),W);
label("$150^\circ$",(0.2,0.4),E);
draw(Z--(0,0)--Y);
draw(X--(0,0));
label("$X$",X,SW);
label("$Y$",Y,NE);
label("$Z$",Z,SE);
[/asy]

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