The Lord is teaching Oliver Cowdery - and all of us - that receiving answers to prayers is often an active process. I do not believe that the Lord wants robots; we are all His children. He doesn't want us to be passive in our own lives.7 Behold, you have not understood; you have supposed that I would give it unto you, when you took no thought save it was to ask me.8 But, behold, I say unto you, that you must astudy it out in your bmind; then you must cask me if it be right, and if it is right I will cause that your dbosom shall eburn within you; therefore, you shall ffeel that it is right.
Whether making an important decision, trying to answer one of life's heavier questions, or whatever it might be, what has worked best for me is to do everything I can to resolve it myself, but always be attentive to direction I receive in response to prayers.
Obviously, this isn't an easy thing to do. The more you think about it and the more you have determined it yourself, the more likely you are to become attached to whatever solution you come up with. However, if we are praying along the way, we can give the Lord many opportunities to guide us throughout the process, as well as many opportunities to seek and express our own humility. Without humility, it is unlikely that we will ask "with a sincere heart, with real intent," and therefore less likely that we'll receive answers to our prayers, and even less likely that we'd follow them if we did receive them.
One example of how active receiving answers to prayers is comes in 1 Nephi 11-15. In these chapters, Nephi is conversing with an angel. Its interesting to note that the angel asks a lot of questions. Many things are not said directly; Nephi is invited to interpret much of what he is shown and told, and then the angel confirms his interpretation. I've never seen an angel, but my experiences receiving answers have been similar.
I've been actively involved in almost all of the most memorable and impactive experiences of my life. The Lord answers our prayers to teach us and direct us, and He invites us to be involved in receiving those answers so it isn't simply in one ear and out the other.
I know first-hand that God answers prayers. Every time I learn more about Him it makes me recognize how much He loves us and wants to talk to us, because we are literally His children. Prayer is among the greatest gifts we have as His children, and I know that He wants all of us to use it.