
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
Find the number of degrees in the measure of angle $y$.

[asy]
import markers;
size (5cm,5cm);
pair A,B,C,D,F,H;

A=(0,0);
B=(5,0);
C=(10,0);
D=(4,8);

F=(2.5,8.2);
H=(5.5,8.2);

draw((4.5,7.1){up}..{right}(5.5,8.2));
draw((3.5,7.1){up}..{left}(2.5,8.2));

draw (A--B--C--D--A);
draw (B--D);

markangle(n=1,radius=8,C,B,D,marker(stickframe(n=0),true));

label ("$y^\circ$", shift(1.3,0.65)*A);
label ("$120^\circ$", shift(1.2,1)*B);
label ("$30^\circ$", F,W);
label ("$21^\circ$",H,E);

[/asy]

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