We discuss a delicate status of advanced interaction in the formalism of the time symmetric AAD approach to simple dynamical problems (motion with the uniform acceleration and the circular-orbit motion). An exclusive (although often unrespected) feature of AAD theory is that no a priori elimination of advanced interaction is in itself admissible. We verify this property on a point-like particle, subjected separately both to the electro-dynamical and linear interactions. The trial proves that such a rigorous requirement of theory has a positive impact on the conservation of inertia principle confirming the fact that the problem of inertia is a physical attribute associated necessarily with the advanced interaction. It is also shown that in the case of weak linear interaction there is a possibility to construct the model of a particle, close to the Wigner free point-like particle, with the internal degrees of freedom that involve both the retarded and advanced components of linear AAD four-potential. In the canonical scenario of model, with constraints on the light cone and the advanced interaction present, there appears as a result of AAD formalism the free-point particle endowed with its trembling motion.