The term 'promote shamelessly' can be summarized by the crossword solution 'FLOG, ' which is a four-letter word meaning to advertise or publicize something aggressively. This term is often used in the context of marketing and sales, where it implies that one should not be ashamed to promote their product or service. It is also used more generally to refer to any kind of promotion or advocacy, such as for a cause or political candidate.