Let $f(x)$ be a polynomial of degree greater than $2$. If $f(1) = 2$ and $f(2) = 3$, find the remainder when $f(x)$ is divided by $(x-1)(x-2)$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $f(x)$ be a polynomial of degree greater than $2$. If $f(1) = 2$ and $f(2) = 3$, find the remainder when $f(x)$ is divided by $(x-1)(x-2)$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
x+1
Let $f(x)$ be a polynomial of degree greater than $2$. If $f(1) = 2$ and $f(2) = 3$, find the remainder when $f(x)$ is divided by $(x-1)(x-2)$.
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