Ich werde meine Entscheidung überdenken. I will think over my decision and then decide if I reconsider it or not. Either yes, I will stick to it or no, I will change it.
Ich soll das Problem nochmal überdenken. In this case you do not just consider between saying 'yes' or 'no', but you think over the whole problem again, the subject matter of the topic.
The difference here lies rather in the nouns (Problem, Entscheidung) and not in the verb.
überdenken - untrennbar
Er dachte über das Problem nach. - nachdenken - trennbar