What single factor should anchor all of your product management efforts?
The pool of prospective customers, and the problems they face, should drive the definition and marketing of your product. However, the anchor for the entire effort is your company's distinctive competence. Your company's distinctive competence is what distinguishes it - and not just your company's products - from existing and potential competitors. It's what your company does or has that no other company has.
Your company's distinctive competence is generally the source of a sustainable competitive advantage. If your company is not uniquely qualified to develop or sell a product that solves problems customers face, then another company can enter the arena and produce or sell the same, or a superior, product.
When you're properly focusing on solving problems in the market, don't forget to ask yourself whether your company is uniquely qualified to solve them. Understand your company's distinctive competence.