Factor completely over the set of polynomials with integer coefficients:
\[x^4 - 4x^3 + 14x^2 - 4x + 13.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Factor completely over the set of polynomials with integer coefficients:
\[x^4 - 4x^3 + 14x^2 - 4x + 13.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(x^2 + 1)(x^2 - 4x + 13)
Factor completely over the set of polynomials with integer coefficients:
\[x^4 - 4x^3 + 14x^2 - 4x + 13.\]
train