
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
On the sides \( AB \) and \( BC \) of an equilateral triangle \( ABC \), points \( L \) and \( K \) are marked, respectively. \( M \) is the intersection point of segments \( AK \) and \( CL \). It is known that the area of triangle \( AMC \) is equal to the area of quadrilateral \( LBKM \). Find the angle \( \angle AMC \).

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