<|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
 Given the curve C: y=3x^4-2x^3-9x^2+4, let l be the tangent line to the curve C at the point M(1, -4). Calculate the number of common points between the tangent line l and the curve C. 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
3
Given the curve C: y=3x^4-2x^3-9x^2+4, let l be the tangent line to the curve C at the point M(1, -4). Calculate the number of common points between the tangent line l and the curve C.
test