<|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
 There are 7 boys and 13 girls standing in a line. Let \( S \) be the number of positions where boys and girls are adjacent to each other. Calculate the average value of \( S \) for all possible arrangements of these 20 people. 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
9
There are 7 boys and 13 girls standing in a line. Let \( S \) be the number of positions where boys and girls are adjacent to each other. Calculate the average value of \( S \) for all possible arrangements of these 20 people. Express your answer as a single integer.
test