solution: In order for the graph to be continuous, the two pieces of the function must meet at $n=a$. In order for this to happen, we know that $4a+3=7a-12$. Solving for $a$, we find that $a=\frac{15}{3}=\boxed{5}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Let \[f(n) =
  \begin{cases}
  4n+3 &\text{if }n<a, \\
  7n-12 &\text{if }n\ge{a}.
  \end{cases}
  \]Find $a$ if the graph of $y=f(n)$ is continuous.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 5
extra_info.question: Let \[f(n) =
  \begin{cases}
  4n+3 &\text{if }n<a, \\
  7n-12 &\text{if }n\ge{a}.
  \end{cases}
  \]Find $a$ if the graph of $y=f(n)$ is continuous.
extra_info.split: test