Counter-checking is a term used to describe the act of verifying and cross-checking information. Its antonyms would therefore be words that imply trusting and accepting information without verifying its accuracy. Synonyms for this would include accepting, acknowledging, believing, and taking at face value. However, it is worth bearing in mind that not counter-checking information can lead to mistakes and misunderstandings. It is therefore important to strike a balance between trusting information and verifying it through careful analysis, research, and cross-referencing with reliable sources. Ultimately, this will help to ensure that accurate information is used to inform decision-making and problem-solving in various contexts.