<|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
 Given the curve C defined by the parametric equations x=1+cosθ and y=sinθ, and the line √3x+y=2√3, calculate the length of the chord AB formed by the intersection of the line and the curve. Express your answer as a single number. 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
1
Given the curve C defined by the parametric equations x=1+cosθ and y=sinθ, and the line √3x+y=2√3, calculate the length of the chord AB formed by the intersection of the line and the curve. Express your answer as a single number.
test