
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]


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An acute-angled triangle \(ABC\) is given. A circle with diameter \(BC\) intersects the sides \(AB\) and \(AC\) at points \(D\) and \(E\) respectively. Tangents drawn to the circle at points \(D\) and \(E\) intersect at point \(K\). Find the angle between the lines \(AK\) and \(BC\).

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