
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 diagonals of the inscribed quadrilateral $ABCD$ intersect at the point $P$, and the triangle $APD$ is acute-angled. Points $E$ and $F$ are the midpoints of sides $AB$ and $CD$, respectively. A perpendicular is drawn from point $E$ to line $AC$, and a perpendicular is drawn from point $F$ to line $BD$; these perpendiculars intersect at point $Q$. Find the angle between lines $PQ$ and $BC$.

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