A phrase I also like to use for what I do is “think alongside.” So I wondered: collaborate: work alongside :: ______: think alongside?
I have spent the last hour in the 1934 Webster’s International in the co- environs, and I recom-mend it if you want to bowl yourself over by how many words include this prefix somewhere in their etymology (*yes, like com-prise!).
Latin, as English, con-tains (yep) co-pious (yep!) words for “think,” but I never found a co- word that nails “think alongside” quite like “collaborate” nails “work alongside.” Com-ment is close, con-sent is close, I love con-fide, but in the end I have to invent (confabulate!) one. “Cogitate” exists and already includes co-, but that co- has lost the “with”ness, so we’ll add another com-(totally ko-sher [no]: con-sider [yep] “co-con-spirator”).
So: concogitate! English mostly uses co- on it’s own when making up (composing!) new words, but Latin would want con- before [c] and I say give Latin what it wants (concede!).