#1. What is Your Goal? Where do you want to end up? What do you mean exactly and precisely when you say that you want to develop your brain to the maximum? What does that mean to you?
Depending on the goal there will be different approaches and different things you need to focus on. Becoming the best version of yourself mentally is all about figuring out what that really means to you and closing the gap between that futuristic version of yourself and your current version; between the ideal and real self. More on that later.
#2. Have a Set Intention. Every day you study, learn, or are in any social situation you should focus on what you want to gain from this situation. What is the one thing you want to achieve in this moment?
Each day should have a maximum of 3 set intentions that give that day a particular theme. But you still want to set an intention as often as you can throughout the day for the little things.
Be flexible enough to change your intention as it works for you, while being strong enough to follow through with your major objective/s throughout the day.
#3. Start thinking outside the Box. Most of the greatest thinkers in the world thought outside the box. They found a new approach to something old that no one has ever thought of before.
The best way to approach this is to start philosophizing about life, the universe or impossible questions of ethics with friends. When you engage in philosophizing, the general rules are that you are accepting of others opinions, that there are no wrong or right answers, and that it is just a discussion of topics no one will know the answer to.
This will get you start to think about big topics in different ways and the more you do this the more you develop your brain to think about even the impossibilities.
Alternatively, or additionally, discuss the topics of your interest with as many knowledgeable individuals as possible. Be open to their opinions on the matter so that you have more information to draw upon.