Lark79: "cuidar" means "to care for, to look after"..............but "cuidad" does not, as far as I know, have a meaning in modern Spanish. It might be the imperative form in Old, Formal Spanish, meaning "Be careful". I do not think it is in use today. It may be something like the language used in Church ritual: for instance, Tomad y bebed de este caliz "Take and drink from this cup" Comed este pan de lo que es mi cuerpo "Eat this bread which is my body"
Cuidad is actually imperative for cuidar in the Vosotros conjugation. Spain is the only place where it's in common use. It means "You" (plural, informal)—think of it as the plural form of tú. Essentially, it's "you guys" or "y'all." The pronoun ustedes is also used in Spain, but not as much, and only for very formal situations. The other verbs you mentioned—tomad, bebed, comed—are also a part of the "Vosotros" conjugation. Learn more about "vosotros" here.
It seems to me that nuevamente here functions as an adverb. Spanishdict.com indicates that nuevamente, as an adverb means "newly, recently, freshly" and NOT "again" (this it supplies as the translation if it were functioning as an adjective).
Hence, it seems to me that the translation above ("I went to the city again.") is incorrect, and that correct English translation include "I newly went to the city" or "I recently went to the city".
Any input from native Spanish speakers here?
Native speaker. I would say Spanishdict.com is wrong in this case. "Nuevamente" always means "(once) again". I can't really think of a situation where "nuevamente" means "newly", and the Real Academia Española (the agreed upon governing body of the Spanish language) says this:
adv. m. Otra vez, de nuevo (once again)
adv. t. desus. Hace poco, recientemente (recently, but "desus" means this definition is no longer in use)
I'm not a native Spanish speaker but as an English speaker I would say that "freshly" often means that something is being done again, with new vigor. Spanishdict.com did NOT indicate that nuevamente does not mean again; that was your misunderstanding. I can see how you made that mistake, though.
I wouldn't say it is necessarily wrong. However, I would consider that the course is trying to teach the term "again" rather than the phrase "once again". Additionally, the phrase "once again" is redundant as just "again" would suffice. However, "once again" can be used to add theatrical emphasis and/or be considered poetic.
Since every answer in the answer bank is entered by hand, there are many potential answers not accounted for. Here are a few examples of answers people might enter as the go through the lesson: "once again", "yet again", "repeatedly". "once more", "anew", "afresh", "another time", "one more time", "de novo", "newly", and so forth.
However, if you report that your answer should be accepted via the Report button in the lesson, just below where it's marked you incorrect, the team might add it to the answer banks the next time they update the tree version. There are simply so many variants to a correct answer, that sometimes they don't think of them all before a particular tree version is launched.