
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, $AB$ is a line segment. A perpendicular line intersects $AB$ at point $C$ and extends to point $D$. Another line intersects $CD$ at point $E$, forming angles with $CD$ such that $\angle DCE$ is directly opposite to $\angle ECA$ and measures $58^\circ$. If $\angle ACD$ is $x^\circ$ and $\angle ECB$ is $y^\circ$, find the values of $x$ and $y$.

[asy]
draw((0,0)--(10,0),black+linewidth(1));
draw((4,0)--(4,8),black+linewidth(1));
draw((4,0)--(3.5,0)--(3.5,0.5)--(4,0.5)--cycle,black+linewidth(1));
draw((4,0)--(9,7),black+linewidth(1));
draw((4,0)--(-1,7),black+linewidth(1));
label("$A$",(0,0),W);
label("$B$",(10,0),E);
label("$x^\circ$",(3.25,2.25));
label("$58^\circ$",(5.5,0.75));
label("$y^\circ$",(-0.5,2.25));
label("$C$",(4,0),S);
label("$D$",(4,8),N);
label("$E$",(9,7),NE);
label("$F$",(-1,7),NW);
[/asy]

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