
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
If $\overline{AD} \| \overline{BC}$, determine the degree measure of angle $EDC$.

[asy]
import olympiad;

pair A = (0,30);
pair B = (-30,0);
pair C = (70,0);
pair D = (0,10);
pair E = (-10,10);

draw(A--D);
draw(B--C);
draw(D--C);
draw(E--C);

label("A", A, N);
label("D", D, NW);
label("B", B, W);
label("C", C, E);
label("E", E, W);

draw(scale(15)*anglemark(C, D, A));
draw(scale(100)*shift(D)*scale(0.1)*shift(-D)*anglemark(B, D, E));
draw(scale(15)*anglemark(C, E, B));

label("$3y$", (35,0), S);
label("$4y$", (-15,5), NW);
label("$5y$", (10,20), NE);
[/asy]

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