<|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 three-digit number \(\overline{abc}\) is a multiple of 15, the two-digit number \(\overline{bc}\) is a multiple of 4, and \(a > b > c\). How many such \(\overline{abc}\) satisfy the given conditions? 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
2
A three-digit number \(\overline{abc}\) is a multiple of 15, the two-digit number \(\overline{bc}\) is a multiple of 4, and \(a > b > c\). How many such \(\overline{abc}\) satisfy the given conditions?
test