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watch (one's) step
1. Literally, to pay attention to where one is walking. This phrase is often used as a command. Watch your step! All of these cords are a tripping hazard.
2. By extension, to proceed with caution. Watch your step when you meet with the boss—this is a situation you need to finesse.
watch one's step
1. be careful of one's walking or stepping. It's slippery here. Watch your step.
2. Fig. to act with care and caution so as not to make a mistake or offend someone. John had better watch his step with the new boss. He won't put up with his lateness. Mary was told by the teacher to watch her step and stop missing classes.