
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 a diagram, triangle ABC is isosceles with $AB=AC$. It is given that $\angle BAC = 36^\circ$. There is a point D inside the triangle such that $\angle ADB = 90^\circ$ and $AD=BD=CD$. Find the measure of $\angle ADC$.

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