
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 $m$ and $n$ are parallel. There is a transversal line which crosses $m$ at a $45^\circ$ angle and line $n$ at a $20^\circ$ angle. Find the measure of angle $y$ in degrees, which is the exterior angle formed by the intersection of line $n$ and an additional line that intersects at a $70^\circ$ angle to line $n$.

[asy]
size(300);
import markers;
pair A = dir(-20)*(0,0);
pair B = dir(-20)*(4,0);
pair C = dir(-70)*(4,2);
pair D = dir(-70)*(0,2);
pair F = dir(-20)*(0,1.3);
pair G = dir(-20)*(4,1.3);
pair H = dir(-20)*(2,1.3);

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=D;
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, red+1bp);

markangle(Label("$45^\circ$",Relative(0.4)),n=1,radius=11,A,C,B);
markangle(Label("$20^\circ$",Relative(0.5)),n=1,radius=11,B,D,C);
markangle(Label("$70^\circ$",Relative(0.4)),n=1,radius=11,B,H,C);

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

[/asy]

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