This is a perfect exercise for getting a small group or a team thinking together.
One person writes the beginning of a sentence and passes it to the next person. He or she adds a few words, then the next person adds a few more, and so on. (The sentence doesn't need to specifically address the problem you're working on. In fact, using a sentence that begins 'Our brand personality is . . . ' would defeat the spirit of the exercise.)
During the exercise, no spoken communication is allowed-let the ideas pop out in your writing. Don't restrain yourself, and don't try to push the writing in any particular direction. You'll be surprised at how quickly the group starts to think on the same wavelength.