
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
Given isosceles triangle \( ABC \) with base \( BC \). Point \( K \) is marked on the extension of side \( AC \) beyond point \( C \), and a circle is inscribed in triangle \( ABK \) with center at point \( I \). A circle that passes through points \( B \) and \( I \) touches line \( AB \) at point \( B \). This circle intersects segment \( BK \) at point \( L \) for the second time. Find the angle between lines \( IK \) and \( CL \). Answer: \( 90^{\circ} \).

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