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>Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: A (very small) ball is kicked off from point A on a square billiard table with side length $2 \mathrm{~m}$. After moving along the shown path and touching the sides three times as indicated, the path ends in point $B$. How long is the path that the bal travels from A to B? (As indicated on the right: incident angle = emergent angle.)
<image1>
Choices:
(A) 7
(B) $2 \sqrt{13}$
(C) 8
(D) $4 \sqrt{3}$
(E) $2 \cdot(\sqrt{2}+\sqrt{3})$ 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
B
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: A (very small) ball is kicked off from point A on a square billiard table with side length $2 \mathrm{~m}$. After moving along the shown path and touching the sides three times as indicated, the path ends in point $B$. How long is the path that the bal travels from A to B? (As indicated on the right: incident angle = emergent angle.)
<image1>
Choices:
(A) 7
(B) $2 \sqrt{13}$
(C) 8
(D) $4 \sqrt{3}$
(E) $2 \cdot(\sqrt{2}+\sqrt{3})$ 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