
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
Let \( AB \) be the diameter of a circle, and \( C \) be a point on the plane. Lines \( AC \) and \( BC \) intersect the circle at points \( M \) and \( N \), respectively. Lines \( MB \) and \( NA \) intersect at point \( K \). Find the angle between lines \( CK \) and \( AB \).

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