
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

In an equilateral triangle \(ABC\), the altitude \(AH\) is drawn. In triangle \(ABH\), point \(I\) is marked at the intersection of the angle bisectors. In triangles \(ABI\), \(BCI\), and \(CAI\), points \(L\), \(K\), and \(J\) are marked respectively at the intersections of the angle bisectors. Find the angle \(KJL\).

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