
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
Each angle of triangle \(ABC\) is an integer degree. There is an obtuse angle at vertex \(A\). The point \(D\) is on side \(BC\) such that triangle \(ABD\) is a right triangle, and triangle \(ADC\) is isosceles. How many such triangles exist? (You do not need to list all the angles of the suitable triangles.)

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