A school district in Seattle used the race of students as a tie$-$breaking factor to determine which students would be admitted to the more popular schools in an attempt to maintain racial diversity. In the case Parents Involved in Community Schools v$.$ Seattle School District No$.1(2007),$ the Supreme Court ruled this plan unconstitutional under the Fourteenth Amendment. Which of the following statements offers the most accurate comparison between this case and the decision in Brown v$.$ Board of Education of Topeka $(1954)?$

a$.$ Both cases involved the use of affirmative action in public schools.

b$.$ Both cases ruled against the school district based on the equal protection clause.

c$.$ Both cases struck down plans to segregate students.

d$.$ Both cases ruled in favor of students based on the due process clause.