Inanely is the adverb of inane: doing something in a hollow, silly way, with little meaning behind it. She smiled inanely — the smile was on her face, but nothing was in it. Someone can also talk inanely, filling time with empty words. Same slightly literary tone as inane; in everyday speech people might say “stupidly” or “blankly,” though those are not exact matches. “Blankly” is closer when there is no thought; “stupidly” is blunter and ruder.