Let $a,$ $b,$ $c,$ $d$ be real numbers such that
\begin{align*}
a + b + c + d &= 1, \\
a + 2b + 4c + 8d &= 16, \\
a - 5b + 25c - 125d &= 625, \\
a + 6b + 36c + 216d &= 1296.
\end{align*}Enter the ordered quadruple $(a,b,c,d).$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c,$ $d$ be real numbers such that
\begin{align*}
a + b + c + d &= 1, \\
a + 2b + 4c + 8d &= 16, \\
a - 5b + 25c - 125d &= 625, \\
a + 6b + 36c + 216d &= 1296.
\end{align*}Enter the ordered quadruple $(a,b,c,d).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(60,-88,25,4)
Let $a,$ $b,$ $c,$ $d$ be real numbers such that
\begin{align*}
a + b + c + d &= 1, \\
a + 2b + 4c + 8d &= 16, \\
a - 5b + 25c - 125d &= 625, \\
a + 6b + 36c + 216d &= 1296.
\end{align*}Enter the ordered quadruple $(a,b,c,d).$
train