What term refers to behaving in a servile manner or lying prostrate?

The term that refers to behaving in a servile manner or lying prostrate is "grovel." This word conveys a sense of deep submission or humility, often employed in contexts where a person is seeking forgiveness or favor. To grovel suggests not only a physical posture of lying down but also a mental state of subservience and desperation to please or appease someone in a position of power.

In contrast, other options do not capture this meaning. "Gullible" describes someone who is easily deceived or tricked, and does not relate to the act of servility. "Heed" refers to paying attention or taking notice, which does not imply any subservient behavior. Lastly, "gust" pertains to a strong burst of wind or emotion and has no connection to the manner of behavior or physical position implied by groveling. Thus, grovel is the most accurate term in this context.