
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
The altitude \( AH \) is drawn to the base \( BC \) of an isosceles triangle \( ABC \). A point \( P \) is marked on side \( AB \) such that \( CP = BC \). Segment \( CP \) intersects the altitude \( AH \) at point \( Q \). It turns out that the area of triangle \( BHQ \) is 4 times smaller than the area of triangle \( APQ \). Find the angles of triangle \( ABC \).

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