
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 side \( AB \) of triangle \( ABC \) there is a point \( K \), and on sides \( AC \) and \( BC \) there are points \( L \) and \( M \) respectively such that \( AK = AL \) and \( BK = BM \). It is found that lines \( LM \) and \( AB \) are parallel. The tangent at point \( L \) to the circumcircle of triangle \( KLM \) intersects segment \( CK \) at point \( D \), and a line passing through \( D \) parallel to side \( AB \) intersects side \( BC \) at point \( E \). Find the angle \( \angle DEO \), where \( O \) is the center of the circumcircle of triangle \( KLM \).

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