When it comes to synonyms for the phrase "attend closely to," there are a variety of options to choose from depending on the context. For instance, "pay close attention to" is a common synonym and can be used interchangeably in most situations. Other similar phrases include "focus on," "heed," "keep an eye on," and "mind." Alternatively, if the context is more specific, other synonyms such as "scrutinize," "inspect," "examine," and "analyze" can be used to convey a more in-depth level of attention being given to a particular subject matter. Overall, selecting the most appropriate synonym will depend on the context and the level of detail required to convey your message accurately.