In the Penitential Act at Mass, all present confess that they have sinned and ask for God's forgiveness. The implication seems to be that everyone present has sinned since the last time they made such an act. Indeed, it seems to me (though I may be mistaken) that the Catholic belief is that everyone still on Earth continues to fall into sin, even if it is in the most minute way.
On the other hand, every sin is an act of free will, and hence avoidable. Since there can be only finitely many acts of free will between penitential acts, this should imply that it is possible to go between penitential acts without sinning at all.
So my question is this: What is the Church's true doctrine concerning the ability of human beings to maintain avoidance of all sin? Does it teach that some do, in fact, maintain avoidance of all sin? Or does it believe that while it is possible to avoid all sin, to do so is so difficult as to be impossible in practical terms? Or is it something else?