For the first slot, the most appropriate option would be "make new connections". This fits the context of a collegial discussion where participants can adapt their views based on effective reasoning from others.
For the second slot, the best option would be "evidence". This fits well with the idea of another person presenting new reasoning that may involve supporting facts or arguments.
So the complete phrase would be: "During a collegial discussion, a participant can make new connections by tweaking their own opinion when another person reasons effectively and presents new evidence."