Let $x,$ $y,$ and $z$ be real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[3x + 4y + 12z.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $x,$ $y,$ and $z$ be real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[3x + 4y + 12z.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
13
Let $x,$ $y,$ and $z$ be real numbers such that $x^2 + y^2 + z^2 = 1.$  Find the maximum value of
\[3x + 4y + 12z.\]
train