Let $p(x)$ be a monic, quartic polynomial, such that $p(1) = 3,$ $p(3) = 11,$ and $p(5) = 27.$  Find
\[p(-2) + 7p(6).\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $p(x)$ be a monic, quartic polynomial, such that $p(1) = 3,$ $p(3) = 11,$ and $p(5) = 27.$  Find
\[p(-2) + 7p(6).\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1112
Let $p(x)$ be a monic, quartic polynomial, such that $p(1) = 3,$ $p(3) = 11,$ and $p(5) = 27.$  Find
\[p(-2) + 7p(6).\]
train