
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
Right triangle $ABC$ with $AB = BC$ is placed such that point $B$ is also a vertex of square $BCDE$. Determine the measure of angle $CAD$.

[asy]
size(70);
draw((0,0)--(20,0)--(20,20)--(0,20)--cycle);
draw((0,20)--(10,0)--(20,20));
draw((10,0)--(20,20));
label("$A$",(10,0),S);
label("$B$",(0,20),W);
label("$C$",(20,20),E);
label("$D$",(20,0),E);
label("$E$",(0,0),W);
[/asy]

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