
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, $AB$ and $CD$ are straight lines. Point $E$ lies on line $CD$. Determine the value of $x$ given that $\angle AXB = 110^\circ$, $\angle CYX = 130^\circ$, and $\angle XYZ = 20^\circ$. Assume $\angle YXE = x^\circ$.
```plaintext
[asy]
draw((0,0)--(12,0));
draw((0,5)--(12,5));
draw((3,0)--(5,5)--(9,0));
label("$110^\circ$",(5,4.5),SW);
label("$130^\circ$",(3,0),NW);
label("$20^\circ$",(7.5,0),N);
label("$A$",(0,5),W);
label("$B$",(12,5),E);
label("$C$",(0,0),W);
label("$D$",(12,0),E);
label("$X$",(5,5),N);
label("$Y$",(3,0),S);
label("$E$",(9,0),S);
label("$x^\circ$",(6,0),SW);
[/asy]
```

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