The phrase "came to power" is the correct and commonly used expression to describe a group assuming control of a government.

Took to" is used when someone develops a habit or interest (e.g., "He took to painting"), so it does not fit this context. "Undertook" means to take on a responsibility or task, but it is not used to describe a government assuming control. "March into" suggests a military movement but is not idiomatic for assuming leadership.