Let's think of a different approach.

Literal

Different method [object-を] think-out [volitional-よう].

考え出す is a compound verb: 考える (think) + 出す (put out) = 'to think up/devise.' The volitional ~よう proposes the action: 'let's come up with one.' 別の方法 is 'a different method/approach.'