They are related but not exactly the same. - 잘 생각하다 - 1) give something a good thought (to make the best decision), 2) try to remember something. - 곰곰이 생각하다 - Ponder something taking time and weighing all aspects in one's mind. (sounds informal) - 신중히 생각하다 - Take something seriously and give it a lot of thoughts with a cautious attitude. (formal) They are often used with the helper verb 보다, which can change the meaning and nuance somewhat. 잘 생각하다 is often used with decision making, because one of 잘's meanings is "for the best outcome". - 잘 생각해 봐 = Think hard to see what's best for you. - 잘 생각했어 or (그건) 잘 생각한 거야 (Yeah, that's probably the right thing/path for you). 곰곰이 and 신중히 describe the attitude and manner. 곰곰이 stresses considering the details one after another, and 신중히 emphasizes being cautious about an important matter.

I think they are interchangeable in almost all situation. but the first one is often used to say "think about it again"