
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 an isosceles triangle \( ABC \), a square is inscribed such that two of its vertices lie on the base \( BC \) and the other two lie on the legs of the triangle. The side of the square is related to the radius of the circle inscribed in the triangle by a ratio of \( 8:5 \). Find the angles of the triangle.

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