
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 vertical line from point \( C \) on \( AB \) meets point \( D \) above \( AB \). Another line segment \( DE \) forms an angle of \( x^\circ \) with line \( CD \) and intersects \( AB \) at point \( E \), creating a \( 60^\circ \) angle with \( AB \). Calculate the value of \( x \).

[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((4,8)--(9,0),black+linewidth(1));
label("$A$",(0,0),W);
label("$B$",(10,0),E);
label("$x^\circ$",(5,4),N);
label("$60^\circ$",(7.5,0.5),E);
label("$C$",(4,0),S);
label("$D$",(4,8),N);
label("$E$",(9,0),S);
[/asy]

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