solution: Multiplying all expressions in the inequalities by $7$, we have $\frac74 < x < \frac73$. Since $\frac 74$ is between $1$ and $2$, and $\frac 73$ is between $2$ and $3$, the only integer $x$ between these two fractions is $\boxed{2}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  What integer $x$ satisfies $\frac{1}{4}<\frac{x}{7}<\frac{1}{3}$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 2
extra_info.question: What integer $x$ satisfies $\frac{1}{4}<\frac{x}{7}<\frac{1}{3}$?
extra_info.split: test