To take for granted or without proof. I assume you have completed the assignment since you didn't ask for an extension.
To take upon oneself; undertake. She assumed the responsibility of organizing the event.
To take on a particular quality, appearance, or role. The chameleon can assume the color of its surroundings.
To begin to have a particular position or status. He will assume the role of CEO next month.
To pretend to have or to put on an appearance of (a quality, feeling, or manner); to feign. He assumed an air of indifference to hide his disappointment.