
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 modified diagram, $AB$ is parallel to $DC,$ and the angle $\angle ACE$ is $100^\circ$. What is the value of $x?$ Given $\angle ADC = 110^\circ$, $\angle ACB = 70^\circ$, and $\angle ABC = 50^\circ$.

[asy]
draw((0,0)--(-.5,5)--(8,5)--(6.5,0)--cycle);
draw((-1,4)--(9,6)); // Change in line angle
label("$A$",(-.5,5),W);
label("$B$",(8,5),E);
label("$C$",(6.5,0),S);
label("$D$",(0,0),SW);
label("$E$",(9,6),N); // Endpoint label shift
draw((2,0)--(3,0),Arrow);
draw((3,0)--(4,0),Arrow);
draw((2,5)--(3,5),Arrow);
label("$x^\circ$",(0.1,4));
draw((3,5)--(4,5),Arrow);
label("$110^\circ$",(0,0),NE);
label("$50^\circ$",(8,5),SW);
label("$70^\circ$",(6.5,0),E);
[/asy]

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