<|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
 The shorter side of a rectangle is equal to 1, and the acute angle between the diagonals is $60^\circ$. Find the radius of the circle circumscribed around the rectangle. 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
The shorter side of a rectangle is equal to 1, and the acute angle between the diagonals is $60^\circ$. Find the radius of the circle circumscribed around the rectangle.
test