
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
Given a circle, inscribe an isosceles triangle with an acute angle. Above one of the legs of this triangle, construct another isosceles triangle whose apex is also on the circumference of the circle. Continue this process and determine the limit of the angles at the vertices of the triangles.

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