<|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 sum of the third binomial coefficient from the start and the third binomial coefficient from the end of the expansion of \((\sqrt[4]{3}+\sqrt[3]{4})^n\) is equal to 9900. How many rational terms are contained in this expansion? 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
The sum of the third binomial coefficient from the start and the third binomial coefficient from the end of the expansion of \((\sqrt[4]{3}+\sqrt[3]{4})^n\) is equal to 9900. How many rational terms are contained in this expansion?
test