
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 given diagram, lines $m$ and $n$ are parallel. Determine the measure of angle $y$ in degrees.

[asy]
size(200);
import markers;
pair A = dir(10)*(0,0);
pair B = dir(10)*(4,0);
pair C = dir(10)*(4,2);
pair D = dir(10)*(0,2);
pair F = dir(10)*(0,1.5);
pair G = dir(10)*(4,1.5);
pair H = dir(10)*(2,1);

markangle(Label("$y$", Relative(0.4)), n=1, radius=11, B, H, C);

pair X,Y;

X=A;
Y=B;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=A;
Y=C;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=C;
Y=B;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=B;
Y=D;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=G;
Y=F;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

label("$n$", 1.4*A-.4*B);
label("$m$", 1.4*F-.4*G);

label("$40^\circ$", A+(1,-.1));
label("$90^\circ$", B+(.4,.1));
label("$40^\circ$", B+(-1,.7));
[/asy]

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