<|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
 A gardener needs to plant three maple trees, four oak trees, and five birch trees in a row. He randomly determines the order in which these trees are planted, with all possible arrangements being equally likely. Let \(\frac{m}{n}\) represent the probability that no two birch trees are adjacent (expressed as a simplified fraction). Find \(m+n\). 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
106
A gardener needs to plant three maple trees, four oak trees, and five birch trees in a row. He randomly determines the order in which these trees are planted, with all possible arrangements being equally likely. Let \(\frac{m}{n}\) represent the probability that no two birch trees are adjacent (expressed as a simplified fraction). Find \(m+n\).
test