You are not going to find purpose by fasting and praying about it. First, purpose is not something lost and obscure. It is not something you will discover by accident. Your purpose is something you learn over time. As you devote yourself to your daily activities, a pattern emerges. There is not enough biblical evidence to support the idea that people should go up to a mountain to pray for purpose and guidance. Sound biblical doctrine is that God will mould you through people that have walked the earth before you. We see then that submission is an important aspect of purpose discovery. You need to be discipled by someone. That is the first step.
Purpose discovery is not about camping up on a mountain, and calling down fire from heaven. It is not about supernatural encounters and experiences. It is about identifying what God is doing in your generation. And understanding your place in the grand scheme of things. Doing the works of him that sent Jesus requires discernment. It is hard to understand divine order without instructions from a human being. You must submit to someone. This kind of discipleship is not a virtual mentoring program. It must be a one-on-one situation. If you want the responsibility of living a purposeful life, also embrace the reality of someone discipling you for many years.
Jesus promised his disciples the Holy Spirit. He assured them that the Spirit will teach them all things. And remind them of things Jesus already taught them. But, we see that the Holy Spirit is not a replacement for human teachers. You still need someone to teach you the basics. You cannot operate in purpose without living a disciplined life. A life that is defined by principles and ideals. And you will be trained in this by a human being. It is self-deceit to insist that the Holy Spirit will teach you every matter of life and purpose. Someone has to disciple you first. Then the Holy Spirit can work in your submissive heart. If your spiritual connection to God is genuine. God will lead you to human beings that will train you, and help you grow into your purpose.