
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
Using drawing and measuring by trial and error, find to the nearest degree the angles of a right-angled triangle whose perimeter is twice the circumference of the inscribed circle. (Describe how you approached the problem, what you kept constant and why, and what you varied until you reached a result.) Also, find the isosceles triangle with the same property.

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