<|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
 Numbers 1 through 9 are written in the cells of a $3 \times 3$ table. All possible sums of the numbers in adjacent (by side) cells are then listed in a notebook. What is the minimum number of different sums that could be listed in the notebook? 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
4
Numbers 1 through 9 are written in the cells of a $3 \times 3$ table. All possible sums of the numbers in adjacent (by side) cells are then listed in a notebook. What is the minimum number of different sums that could be listed in the notebook?
test