You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>In the diagram below of circle $O$, chords $\overline{A B}$ and $\overline{C D}$ intersect at $E$.<image 1>If $C E=10, E D=6$, and $A E=4$, what is the length of $\overline{E B}$ ?
A. 15
B. 12
C. 6.7
D. 2.4

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
A
In the diagram below of circle $O$, chords $\overline{A B}$ and $\overline{C D}$ intersect at $E$.<image 1>If $C E=10, E D=6$, and $A E=4$, what is the length of $\overline{E B}$ ?
A. 15
B. 12
C. 6.7
D. 2.4

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val