solution: There are $8!$ ways to place the people around the table, but this counts each valid arrangement 4 times (if you move each person 2, 4, or 6 places clockwise you get the same arrangement).  The answer is $\dfrac{8!}{4} = \boxed{10080}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  In how many ways can 8 people be seated around a square table with 2 people on a side?  (Two configurations are considered equivalent if one is a rotation of another.)
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 10080
extra_info.question: In how many ways can 8 people be seated around a square table with 2 people on a side?  (Two configurations are considered equivalent if one is a rotation of another.)
extra_info.split: test