What is the coefficient of $x^2y^2$ in the expansion of $(x+y)^4+(x+2y)^4$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the coefficient of $x^2y^2$ in the expansion of $(x+y)^4+(x+2y)^4$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
30
What is the coefficient of $x^2y^2$ in the expansion of $(x+y)^4+(x+2y)^4$?
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