
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 an inscribed quadrilateral $ABCD$ intersect at point $P$, and triangle $APD$ is acute. Points $E$ and $F$ are the midpoints of sides $AB$ and $CD$, respectively. A perpendicular from point $E$ is drawn to line $AC$, and a perpendicular from point $F$ is drawn 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