Feign (verb) - Pretend to be affected by (a feeling, state, or injury)/ make believe with the intention of deceiving.
Synonym: Simulate, Fake, Sham, Give the appearance of, Make a show of, Make a pretence of.
Example: I feign sleep when Mom checks up on me after bedtimes, then I go back to playing video games when she leaves.
Fain (adjective) - pleased or willing under the circumstances/ pleased or inclined to do something.
Adverb – Gladly
Synonym: Eager, Inclined, Pleased.
Example: The kind priest was fain to offer shelter to the homeless man.