The term 'solemnly affirm' is a phrase used to express a serious commitment or promise. It can be broken down into two crossword solutions: 'AVOW' (4 letters) and 'swear to' (7 letters). AVOW is defined as to declare openly and firmly, while swear to is defined as to make a solemn promise or pledge. Together, these two words form the phrase 'solemnly affirm, ' which is used to express a serious commitment or promise.