
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, line $m$ and line $n$ are parallel, and a transversal intersects them making an angle of $45^\circ$ with line $m$. Find the measure of angle $y$ in degrees, where $y$ is the obtuse angle adjacent to $45^\circ$ on the same side of the transversal.
```
[asy]
size(200);
import markers;
pair A = (0,0);
pair B = (4,0);
pair C = (4,2);
pair D = (0,2);
pair E = (0,1);
pair F = (4,1);
pair G = (3,0);  // Transversal intersection on k
pair H = (3,2);  // Transversal intersection on l

draw(A--B, red);
draw(D--C, red);
draw(G--H, blue);
label("$n$", 1.4*D-0.4*C);
label("$m$", 1.4*A-0.4*B);
label("$45^\circ$", G+(0,-0.4), SE);
label("$y$", G+(0.3,0.4), NE);

markangle(Label("$45^\circ$",Relative(0.5)), radius=15, G,H,H-A);
markangle(Label("$y$",Relative(0.5)), radius=30, H-A,H,G);
[/asy]
```

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