The correct answer is a) prophase.
During prophase, several key events occur as the cell prepares to divide. Firstly, the nuclear membrane breaks down, which allows the genetic material to be accessed. Secondly, the chromatin, which is the material made of DNA and protein, condenses into visible chromosomes. This condensation is crucial because it makes the chromosomes easier to separate later in the process. Additionally, the centrioles, which are structures involved in the organization of microtubules, start moving towards opposite poles of the cell. This movement is essential for the formation of the mitotic spindle, which will help segregate the duplicated chromosomes during the later stages of cell division.