
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 that $\overline{AD} \| \overline{FG}$, and assuming that $\angle CFG = 2x$, $\angle CEA = 3x - 20^\circ$, and $\angle AEB = x + 30^\circ$, find the measure of $\angle EFG$.

[asy]
import olympiad;

pair A = (-15,20);
pair B = (-12,35);
pair C = (35,50);
pair D = (35,20);
pair E = (14,20);
pair F = (0,0);
pair G = (40,0);

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

label("F", F, W);
label("G", G, ENE);
label("C", C, N);
label("A", A, W);
label("D", D, ENE);
label("E", E, SE);
label("B", B, NW);

draw(scale(20)*anglemark(G, F, C));
draw(shift(E)*scale(35)*shift(-E)*anglemark(B, E, A));
draw(shift(E)*scale(20)*shift(-E)*anglemark(C, E, B));

label("$x$", (6,20), NW);
label("$3x-20^\circ$", (13,25), N);
label("$2x$", (5,0), NE);
label("$x+30^\circ$", (13,40), N);
[/asy]

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