solution: Let $r_1, r_2$, and $r_3$ be the roots. Then \[
  5= \log_2r_1 + \log_2 r_2 + \log_2 r_3 = \log_2r_1r_2r_3,
  \]so $r_1r_2r_3 = 2^5 = 32$. Since \[
  8x^{3}+4ax^{2}+2bx+a=8(x-r_1)(x-r_2)(x-r_3),
  \]it follows that $a = -8r_1r_2r_3= \boxed{-256}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  For some real numbers $a$ and $b$, the equation \[
  8x^3 + 4ax^2 + 2bx + a = 0
  \]has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of $a$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: -256
extra_info.question: For some real numbers $a$ and $b$, the equation \[
  8x^3 + 4ax^2 + 2bx + a = 0
  \]has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of $a$?
extra_info.split: test