
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
Isosceles triangle $ABC$ and rectangle $BCDE$ are coplanar, with $AB = AC$ and $BC = DE = EB = CD/2$. Calculate the measure in degrees of angle $CAD$.

[asy]
size(100);
draw((0,0)--(40,0)--(40,20)--(0,20)--cycle);
draw((0,20)--(20,60)--(40,20));
draw((20,60)--(40,0));
label("$A$",(20,60),N);
label("$B$",(0,20),W);
label("$C$",(40,20),E);
label("$D$",(40,0),E);
label("$E$",(0,0),W);
[/asy]

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