
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
The diameter \( AB \) and the chord \( CD \) of a circle intersect at point \( E \), such that \( CE = DE \). Tangents to the circle at points \( B \) and \( C \) intersect at point \( K \). Segments \( AK \) and \( CE \) intersect at point \( M \). Find the area of triangle \( CKM \) if \( AB = 10 \) and \( AE = 1 \).

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