Neo-Advaita picked up this teaching from traditional Vedanta. It is called neti neti, not this, not that. Bascially, all that Neo-Advaita has is neti neti, but it is not actually properly understood by the teachers. Negating the mind can take you quite a way, but it cannot close the deal because the denial of the apparent reality is not tantamount to the hard and fast realization “I am limitless non-dual ordinary actionless awareness.” And the removal of the apparent is not accomplished by BELIEVING in this teaching, by mindless denial. It only comes about by intense self inquiry, applying inquiry to everything that happens in you on a moment to moment basis.
This apparent reality teaching is quite sophisticated and I cannot do it justice here. James Swartz Interview in non-dualitymagazine (capital letters added)