
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 triangle $ABC$ with point $D$ on line segment $AB$, the segments satisfy $AD = DC = CB$, and the measure of angle $ACB$ is 90 degrees. What is the number of degrees in the measure of angle $CAD$?

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