<|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 wants to plant three maple trees, four oak trees, and five birch trees in a row. He randomly determines the arrangement of these trees, and each possible arrangement is equally likely. Let the probability that no two birch trees are adjacent be represented by \(\frac{m}{n}\) in simplest form. 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 wants to plant three maple trees, four oak trees, and five birch trees in a row. He randomly determines the arrangement of these trees, and each possible arrangement is equally likely. Let the probability that no two birch trees are adjacent be represented by \(\frac{m}{n}\) in simplest form. Find \(m+n\).
test