solution: The only handshakes at the arcane mixer were between the $6$ witches and $10$ sorcerers, so there were $6 \cdot 10 = \boxed{60}$ handshakes at the mixer.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Six witches and ten sorcerers are at an arcane mixer. The witches have decided to shake hands with each of the sorcerers. None of the witches bothered to shake each other's hands, since they are all good friends already, and the sorcerers all sort of hate each other and did not shake hands with other sorcerers. How many handshakes took place at the mixer?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 60
extra_info.question: Six witches and ten sorcerers are at an arcane mixer. The witches have decided to shake hands with each of the sorcerers. None of the witches bothered to shake each other's hands, since they are all good friends already, and the sorcerers all sort of hate each other and did not shake hands with other sorcerers. How many handshakes took place at the mixer?
extra_info.split: test