
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 the diagram below, $\overline{AB}\parallel \overline{CD}$ where lines $\overline{EF}$ and $\overline{GH}$ intersect lines $\overline{AB}$ and $\overline{CD}$ at points $X$ and $Y$ respectively. It is given that $\angle AXE$ is $120^\circ$ less than 4 times $\angle CYX$. Find $\angle BXY$.

[asy]
unitsize(1inch);
pair A,B,C,D,X,Y,E,F,G,H;
A = (0,0);
B = (1,0);
C = (0,0.8);
D = (1,0.8);
E = (0.3,-0.2);
F = (0.7,1);
G = (0.2, -0.3);
H = (0.8, 1.1);
draw(E--F);
draw(A--B);
draw(C--D);
draw(G--H);
label("$E$",E,S);
label("$F$",F,N);
label("$G$",G,S);
label("$H$",H,N);
X = intersectionpoint(A--B, E--F);
Y = intersectionpoint(C--D, G--H);
label("$X$",X,S);
label("$Y$",Y,N);
label("$A$",A,W);
label("$B$",B,E);
label("$C$",C,W);
label("$D$",D,E);
dot(X);
dot(Y);
dot(E);
dot(F);
dot(G);
dot(H);
[/asy]

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