
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
Point \( O \) is the center of the circumcircle of triangle \( ABC \). Points \( Q \) and \( R \) are chosen on sides \( AB \) and \( BC \), respectively. Line \( QR \) intersects the circumcircle of triangle \( ABR \) again at point \( P \) and intersects the circumcircle of triangle \( BCQ \) again at point \( S \). Lines \( AP \) and \( CS \) intersect at point \( K \). Find the angle between lines \( KO \) and \( QR \).

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