
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
Given the diagram below, find the number of degrees in the measure of angle $x$.

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

A=(0,0);
B=(5,0);
C=(9,0);
D=(3.8,7);

F=(2.3,7.2);
H=(5.3,7.2);

draw((4.2,6.1){up}..{right}(5.3,7.2));
draw((3.6,6.1){up}..{left}(2.3,7.2));

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

markangle(n=1,radius=9,C,B,D,marker(stickframe(n=0),true));

label ("$x^\circ$", shift(1.3,0.65)*A);
label ("$124^\circ$", shift(1.2,1)*B);
label ("$30^\circ$", F,W);
label ("$28^\circ$",H,E);
[/asy]

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