<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 A dog is tied to a tree by a long nylon cord. There is a triangular-shaped obstacle nearby, with its vertices situated at points A, B, and C, where point A lies on the north side of the tree, point B is 10 feet directly east of point A, and point C is 20 feet diagonally southeast of point A. The dog starts at point A and runs around the triangular obstacle to finally reach point D, the due south side of the tree. During its run, the nylon cord is extended to its full length at all times without interfering with the obstacle. If the dog traveled approximately 60 feet, what was the approximate length of the nylon cord, L, in feet? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
30
A dog is tied to a tree by a long nylon cord. There is a triangular-shaped obstacle nearby, with its vertices situated at points A, B, and C, where point A lies on the north side of the tree, point B is 10 feet directly east of point A, and point C is 20 feet diagonally southeast of point A. The dog starts at point A and runs around the triangular obstacle to finally reach point D, the due south side of the tree. During its run, the nylon cord is extended to its full length at all times without interfering with the obstacle. If the dog traveled approximately 60 feet, what was the approximate length of the nylon cord, L, in feet?
test