to assume a certain role, task, or position means to take it on and become responsible for it.
1. The new CEO assumed control of the company.
2. I assumed responsibility for the project.
3. He assumed the position of team leader.
When using the verb form of 'assume,' it's important to remember that it must be paired with an object (i.e., responsibility, position, task, role, etc.). Thus, when using it in a sentence, make sure there is something immediately after it that explains further what is being assumed.