The verb induce means to persuade or influence someone to do something.

Synonyms are encourage, activate, breed, or urge.

The word origins from Latin (late 14th century) inducere meaning “lead into, bring in, introduce, conduct, persuade, suppose, imagine”. It comes from in– meaning “into, in, on, upon” plus ducere meaning “to lead”. Its meaning “to bring about” in any way (in reference to a trance, a fever, etc.) is from the early 15th century. Its sense of “to infer by reasoning” is from 1560s.

I would do anything to induce them to speak up.

More than two-thirds of the company’s population were induced to take the drug test.

Studies show Oxycontin induces labor.