The phrase "keep track of" implies monitoring or observing something in order to stay up-to-date and informed. There are several alternative words and phrases that can be used in its place, depending on the context. Here are some examples: track, monitor, follow, observe, supervise, oversee, manage, watch, keep an eye on, keep tabs on, maintain records of, and stay informed about. Each of these synonyms highlights a slightly different aspect of the original phrase, from actively overseeing or managing to simply paying attention and staying informed. The choice of synonym will depend on the specific context and emphasis of the sentence or task at hand.