<|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
 Given 8 planes in space, for each pair of planes, the line of their intersection is noted. For each pair of these noted lines, the point of their intersection is noted (if the lines intersect). What is the maximum number of noted points that could be obtained? 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
56
Given 8 planes in space, for each pair of planes, the line of their intersection is noted. For each pair of these noted lines, the point of their intersection is noted (if the lines intersect). What is the maximum number of noted points that could be obtained?
test