The term 'reason out' can be defined as the process of logically analyzing a situation in order to come to a conclusion. This term can be broken down into four crossword solutions: DEDUCE (6 letters), INFER (5 letters), DERIVE (6 letters), and EDUCE (5 letters). Deducing is the process of arriving at a conclusion based on evidence or facts. Inferring is the process of drawing a conclusion from available information. Deriving is the process of obtaining something from a source. Finally, educing is the process of bringing out or eliciting something from a source. All of these processes involve using logic to come to a conclusion, which is the definition of 'reason out'.