Discovering and assimilating new information is one way to train your brain. The key is the assimilation part. Gathering information isn't enough. Learning to integrate the new information in a way that broadens or deepens your original thoughts takes effort and a willingness to alter your thinking.
One way to apply brain training to writing is sharing your work with others and learning to assimilate feedback in a way that improves your work. This takes practice and more practice. You will falter, stumble and fall numerous times before you are able to get up and do the work that needs to be done.