How did John Stuart Mill agree with Auguste Comte about social science?

Auguste Comte and John Stuart Mill shared a fundamental agreement regarding the possibility of a genuine social science.1

Both thinkers believed that it is possible to apply the principle of causation and the methods of physical science to the study of moral and social phenomena. While Mill acknowledged that social phenomena are often so complex that they may only yield "conditional predictions," he maintained, in agreement with Comte, that such study could lead to the discovery of valid "social laws".1

This shared perspective was rooted in their mutual commitment to empirical inquiry, though it is important to note that Mill and Comte held distinct philosophical views in other areas, and Mill is often categorized as a liberal thinker who maintained his own independent approach to logic and ethics.21