<|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
 In the cube $ABCD-A_1B_1C_1D_1$, how many line segments (including edges, face diagonals, and space diagonals) are perpendicular to edge $AB$? Provide your answer as a whole number. 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
12
In the cube $ABCD-A_1B_1C_1D_1$, how many line segments (including edges, face diagonals, and space diagonals) are perpendicular to edge $AB$? Provide your answer as a whole number.
test