solution: If we look at the terms of the sequence mod 4, we see that they follow a pattern of period 6: \begin{align*}
  F_1 &\equiv 1\pmod{4}, \\
  F_2 &\equiv 1\pmod{4}, \\
  F_3 &\equiv 2\pmod{4}, \\
  F_4 &\equiv 3\pmod{4}, \\
  F_5 &\equiv 1\pmod{4}, \\
  F_6 &\equiv 0\pmod{4}, \\
  F_7 &\equiv 1\pmod{4}, \\
  F_8 &\equiv 1\pmod{4},~\ldots
  \end{align*} Then we see that the terms repeat.  Therefore, the $100^{\text{th}}$ term is the same as the $4^{\text{th}}$ term, and thus has a remainder of $\boxed{3}$ when divided by 4.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, $\ldots$ where each term is the sum of the previous two terms. What is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 4?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 3
extra_info.question: The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, $\ldots$ where each term is the sum of the previous two terms. What is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 4?
extra_info.split: test