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The concept of moral certitude may be helpful here. As defined in the Catholic Encyclopedia article on Certitude,
Moral certitude is that with which judgments are formed concerning human character and conduct; for the laws of human nature are not quite universal, but subject to occasional exceptions.
Moral certitude is distinguished from metaphysical certitude (e.g., 2+2=4). Given the harmful effects of original sin (i.e., a weakened will and a darkened intellect), I have a moral certitude that I will sin in the future.
Fr. Alfred Wilson, in his excellent book Pardon and Peace, sums up our situation nicely:
The wise man says: “I shall most likely fall again, but I am going to do my very best not to fall.”
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The Council of Trent, the most important Council of the Church when speaking of the true nature of justification (i.e. because it was in response to the Protestant heresy which principally denied it), taught the following infallibly:
If any one saith, that a man once justified can sin no more, nor lose grace, and that therefore he that falls and sins was never truly justified; or, on the other hand, that he is able, during his whole life, to avoid all sins, even those that are venial, — except by a special privilege from God, as the Church holds with regard to the Blessed Virgin; let him be anathema.
So quite clearly it is not possible to avoid all venial sin, except by a special or unique grace and privilege of God which, as it is implied here, was only given to the immaculately conceived mother of God, the new Eve.