
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
There are two circles: one with center at point \( A \) and radius 6, and the other with center at point \( B \) and radius 3. Their common internal tangent touches the circles respectively at points \( C \) and \( D \). The lines \( AB \) and \( CD \) intersect at point \( E \). Find the length of \( CD \), given that \( AE = 10 \).

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