Я считаю = Я думаю = Я полагаю = По-моему = In my opinion = I think However, "Я думаю" can be used like description of process: Teacher : It is time to give an answer. Are you ready? (Пора отвечать. Вы готовы?) Student : Could you give me two minutes, please? I'm still thinking (Не могли бы Вы мне дать 2 минуты, пожалуйста? Я все еще думаю) :)

Hey, Paula! These verbs are synonyms. In my opinion, "Я считаю" sounds more formally ( ="i consider", "i suppose"). "Я думаю" means simply "i think"

"Я считаю" means you have an opinion regarding something. "Я думаю" can mean an opinion as well, but could be also just "I think". For example "what are you doing now?" - "Я думаю", or "I think how to solve the question" - "Я думаю над решением задачи". When we mean an opinion we usualy use "что" - "Я думаю, что ... ", for example "Я думаю что на улице холодно" = "Я считаю что на улице холодно".

Thank you so much for the answers! All of them are excelent and clarifying!

"я считаю" --- more confident