Categorically bounded free recall is a fundamental, yet poorly understood capability of human behavior. Thus, we are able to easily engage in spontaneous generative thought processes while constraining them within specific categorical boundaries. For example, easily and freely come up with names of famous politicians while avoiding the intrusions of names of places or movie actors. Previous research has uncovered a neuronal baseline shift mechanism by which ultra-slow spontaneous fluctuations in activity of neurons, participating in the targeted category, get amplified; thus, increasing their probability of crossing the decision bound and initiating the spontaneous event. However, it is not clear how, mechanistically, such amplification may take place in the brain. More generally, it is still unknown how the observed ultra-slow time scales of the scale-free spontaneous fluctuations spectrum emerge out of the typically fast time scales of cortical neurons. Here we show, using a model of a simple random recurrent neuronal network, with its parameters preset near the dynamical phase transition point, that such selective amplification of slow frequencies can be simulated by a small shift of the network closer to its critical point. Hence, an observed byproduct of a shift towards the dynamical phase transition point is the, so called, "critical slowing down" phenomenon. Furthermore, using simple and physiological parameter fitting, with an input consisting of stochastic white noise to the network's neurons, we precisely simulate the ultra-slow spontaneous fluctuations observed during rest and an intrinsic recall process in the human cortex. Our results illustrate how the complex spontaneous fluctuations observed in the human brain can be explained by a simple, stochastically driven, recurrent network which operates near a critical point. They also provide a ready neuronal mechanism accounting for the remarkable ability of the human brain to set categorical boundaries rapidly and flexibly through amplification of the slow frequencies of the spontaneous, resting state, fluctuations during targeted free behaviors.