<|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
 Several circles are positioned in the plane such that there are exactly 12 points where at least two circles intersect. What is the minimum number of regions into which these circles divide the plane? 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
14
Several circles are positioned in the plane such that there are exactly 12 points where at least two circles intersect. What is the minimum number of regions into which these circles divide the plane?
test