"Gumshoed" is a colloquial term which means to investigate or snoop around. There are several other synonyms for this word, such as sleuthed, probed, pried, spied, snooped, and scrutinized. These words all convey a sense of stealth and clandestine investigation, often associated with detective work. The word "sleuthed" refers to the work of a detective who tracks down clues to solve a mystery while "probed" means to explore or examine something carefully. "Pried" indicates an intrusive investigation whereas "spied" involves observation secretly. "Snooped" means to investigate with the intention of finding out secret information while "scrutinized" implies careful analysis of a person or situation.