<|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
 Different patterns can be created by shading exactly three of the nine small triangles shown, no two of which can share a side. Patterns that can be matched by rotations or by reflections are considered the same. How many different patterns can be created? Express your answer as a single integer. 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
10
Different patterns can be created by shading exactly three of the nine small triangles shown, no two of which can share a side. Patterns that can be matched by rotations or by reflections are considered the same. How many different patterns can be created? Express your answer as a single integer.
test