
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 height $A H$ is drawn from the vertex $A$ to the base $BC$ of isosceles triangle $ABC$. A point $P$ is marked on the side $A B$ such that $C P = BC$. The segment $C P$ intersects the height $A H$ at point $Q$. It turns out that the area of triangle $BH Q$ is 4 times smaller than the area of triangle $AP Q$. Find the angles of triangle $ABC$.

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