<|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
 Let \( S = \{1, 2, 3, 4\} \). A sequence of \( n \) terms \( a_1, a_2, \cdots, a_n \) has the following property: for any non-empty subset \( B \) of \( S \) (denote the number of elements in \( B \) as \( |B| \)), there exist \( |B| \) adjacent terms in the sequence that exactly form the subset \( B \). Find the minimum value of \( n \). 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
8
Let \( S = \{1, 2, 3, 4\} \). A sequence of \( n \) terms \( a_1, a_2, \cdots, a_n \) has the following property: for any non-empty subset \( B \) of \( S \) (denote the number of elements in \( B \) as \( |B| \)), there exist \( |B| \) adjacent terms in the sequence that exactly form the subset \( B \). Find the minimum value of \( n \).
test