
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, lines $k$ and $\ell$ are parallel. The angles given at certain points take different measures. Find the measure of angle $y$ in degrees.

[asy]
size(200);
import markers;
pair A = dir(-22)*(0,0);
pair B = dir(-22)*(4,0);
pair C = dir(-22)*(4,2);
pair D = dir(-22)*(0,2);
pair F = dir(-22)*(0,1.3);
pair G = dir(-22)*(4,1.3);
pair H = dir(-22)*(2,1);

//markangle(.3,B,H,C);
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("$\ell$",1.4*A-.4*B);
label("$k$",1.4*F-.4*G);

label("$45^\circ$",A+(1,-.1));
label("$90^\circ$",B+(.4,.1));
label("$45^\circ$",B+(-1,.7));
[/asy]

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