
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
A circle is inscribed in a triangle, and the points of tangency with the sides of the triangle are connected to each other. A new circle is inscribed in the resulting triangle, and the points of tangency with its sides are the vertices of a third triangle, which has the same angles as the original triangle. Find these angles.

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