The term 'avoiding detection by moving carefully' can be summarized by the crossword solutions ELUDE (5 letters), EDGING (6 letters), RADAR (5 letters), sonar (5 letters), and EASE (4 letters). ELUDE means to escape or avoid, while EDGING is a slow and cautious movement. RADAR and sonar are both methods of detecting objects from a distance, with RADAR using radio waves and sonar using sound waves. EASE is a gradual and gentle manner of doing something. Therefore, the term 'avoiding detection by moving carefully' can be summarized as escaping or avoiding detection by making slow and cautious movements in a gradual and gentle manner.