
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
Point \( E \) lies on the extension of side \( AC \) of equilateral triangle \( ABC \) beyond point \( C \). Point \( K \) is the midpoint of segment \( CE \). The line passing through point \( A \) perpendicular to \( AB \) and the line passing through point \( E \) perpendicular to \( BC \) intersect at point \( D \). Find the angles of triangle \( BKD \).

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