I was wondering if anyone could explain the nuances between 그렇다 and 그러다 when they have principles attached to them. In most cases, they end up having the same spelling and through context you can tell which one it is, but I have come across examples online where the 그래 for example is attributed to 그렇다 when it seems closer to 그러다. I might be overthinking all of this but I'd like to know if there is a clear distinction or not. There are other examples (like HowToStudyKorean) where everything is attributed to 그렇다 but I'm not sure if that's just the teacher's way of simplifying things.
A. 내일 공원에 같이 가고 싶어?
B. 그래. 같이 가
I would assume, because 그래 isn't just an agreement but an agreement to performing an action, that this is 그러다.
A. 이 물이 맛이 없어
B. 그럴까?
I would assume that the 그럴까 in the example above is saying something like "oh is that so?" so it's 그렇다 and the example below is saying "shall we do it?" so it's 그러다.
A. 집에 늦게 갈래?
B. 그럴까?
Is this the right way to think of these responses or are they all really just 그렇다? Or am I overthinking things?