Writing is a way to solve problems. If you master it, your words will carry healing powers. Your societal responsibility as a writer is about doing your best to nurture them.
How you approach problem-solving in your writings depends on your preferred genre.
I like the approach of most self-help books. Each section treats one sub-problem and can be subdivided into four parts.
The first part is about stating important facts. Those first principles have to be interesting to your readers: large enough to be acknowledge as an universal truth, but niche enough to be new and exciting to learn.
Each fact describes a reality, and problems arise when realities collide. The second phase describes this paradox: what it is, and why it's important to solve. The book I'm currently reading, Digital Minimalism by Cal Newport, is a great example of that. Technology consumes a large part of our days, it's both a positive force and a threat to individuality: how do we make the best of our digital lives?
Then comes the actual solution. This is where the writer gets to bring out most of the book's value proposition.
Of course, stating a solution is not enough. It has to be backed by research, experiments, and proofs. The last part should be about demonstrating its effectiveness.
In other words, effective problem-solving writing in the non-fiction genre follows a scientific method.