
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 $\triangle XYZ$, $XZ = YZ$, $m\angle DYZ = 50^\circ$, and $DY \parallel XZ$. Determine $m\angle EDY$ where point $E$ lies on line $XZ$ extending beyond $X$.

[asy]
pair X, Y, Z, D, E;
X = dir(130); 
Y = dir(50); 
Z = (0,0);
D = (0.5,0);
E = (-1,0);
draw(Y--Z--X--cycle, blue);
draw(X--E, red);
draw(Y--D, red);
label("$X$", X, NW);
label("$Y$", Y, NE);
label("$Z$", Z, S);
label("$D$", D, E);
label("$E$", E, W);
[/asy]

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