
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
A circle is circumscribed around an acute-angled triangle \(ABC\). Point \(K\) is the midpoint of the smaller arc \(AC\) of this circle, and point \(L\) is the midpoint of the smaller arc \(AK\) of this circle. The segments \(BK\) and \(AC\) intersect at point \(P\). Find the angle between the lines \(BC\) and \(LP\), given that \(BK = BC\).

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