What is the minimum value of the expression $2x^2+3y^2+8x-24y+62$ for real $x$ and $y$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the minimum value of the expression $2x^2+3y^2+8x-24y+62$ for real $x$ and $y$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
What is the minimum value of the expression $2x^2+3y^2+8x-24y+62$ for real $x$ and $y$?
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