Taken from the live session this week, I'd like to comment a bit about music as I can't say much at all about dancing. :)
Being heavily into music growing up, I'd like to offer one perspective with regard to creativity and critical thinking.
I agree that they are separate processes but they do coexist. Playing bass guitar in a variety of musical contexts (i.e., classic, rock, jazz, musicals, etc.), there were always varying degrees of creativity and critical thinking required. Playing classical music involves more critical thinking skills such as playing in tune and playing musically. Since most of the interpretation of the music was already predetermined by the director and/or the composer, the creative "juices" still existed but were limited within the parameters of the musical composition. Listening to two different orchestras perform Adagio for Strings the expert will notice slight differences in interpretation, and it's these differences that link back to both critical and creative thinking. That is, with gained knowledge and understanding of music, one uses their critical thinking skills to detect periods of creativity.
Now playing jazz music (i.e., standard jazz originating from the 20s-50s) is a different story and is more indicative of how we communicate. Jazz music during this time was known for it's improvisation and creative style that allows musicians to play off each other. When jazz musicians are improvising a solo, for example, there is a high degree of creativity that is required. But at the same time, they are also being critical in listening to the chord changes, the way in which other musicians are playing, etc. Both processes are occurring at the same time, even though one can be more critical upon hearing a recording of a performance after the fact.
Someone just starting to learn how to play jazz music, specifically how to improvise a given set of chord changes, will be less creative and less critical because they have a naive view of what scales to play, playing in tune, finger positions, etc. Once the musician becomes more proficient, knowing what scales to play, playing in tune, etc. becomes second nature, freeing them up to be more creative and thus allowing them to be more critical as well (playing in tune, following what the solo, respecting the musical integrity of the song, etc.).
Moving away from music now and looking at brainstorming, the level of creativity and critical thinking skills are also related. If I am brainstorming about a topic that I know little about, then it will be difficult for me to be critical (and even creative) as I come up with ideas. As I learn more about the topic, I will be able to become more creative and critical about the topic because I will be able to make a more thorough argument.
When building a house, if I am being creative in choosing the right tile for the kitchen, the paint for the living room, etc., then later realize that I am over budget (i.e., using critical thinking skills), I basically just have a lack of knowledge as to what it takes to build a house. The next time I build a house I will have learned more about cost and design and that will influence the decisions I make in the future, causing me to be more critical and creative at the same time: like realizing that I can mix an expensive tile with a cheaper tile that actually looks better but is less expensive to install.
Even though we use creative and critical thinking skills at the same time, reflection can (not always) provide an additional perspective that can add to the critical thinking process.