<|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
 The numbers \(1, 2, 3, \ldots, 7\) are randomly divided into two non-empty subsets. What is the probability that the sum of the numbers in the two subsets is equal? If the probability is expressed as \(\frac{p}{q}\) in its lowest terms, find \(p + q\). 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
67
The numbers \(1, 2, 3, \ldots, 7\) are randomly divided into two non-empty subsets. What is the probability that the sum of the numbers in the two subsets is equal? If the probability is expressed as \(\frac{p}{q}\) in its lowest terms, find \(p + q\).
test