
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 $ABR$ a second time at point $P$ and intersects the circumcircle of triangle $BCQ$ a second time 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}
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