The phrase "blundered on" implies a sense of clumsiness or carelessness in one's actions. Antonyms for this phrase may include words such as "deliberated," "thoughtfully," or "strategically." These words connote a sense of careful consideration and planning in one's actions, rather than simply stumbling blindly forward. Other antonyms might include words such as "decisively," "confidently," or "intentionally." Each of these words suggests a level of purposefulness and determination in one's actions, as opposed to the aimless wandering that is suggested by the phrase "blundered on." Ultimately, the choice of antonym will depend on the tone and context of the sentence in which it appears.