Which of the following statements are correct:
A. In bacteria, RNA primers are removed by the action of polymerase II.
B. In bacteria, polymerase III synthesizes both leading and lagging strands of DNA.
C. In eukaryotes, Polymerase $\delta$ is responsible for synthesis of the lagging strand.
D. In eukaryotes, Polymerase $\varepsilon$ is responsible for synthesis of leading strands.