From a system theory perspective, p53 network dynamics is interesting since it can exhibit three dynamical modes of p53, namely low-level equilibrium, oscillation, and high-level equilibrium. Each of these modes are associated with different cell fate outcomes: cell survival, cell cycle arrest, and apoptosis. The literature reveals that a high level (apoptosis) is seen only after ending the oscillation phase, so called two-phase dynamics, which provides the decision of apoptosis depending on the oscillation duration. This paper proposes that a negative feedback can keep time by counting the pulses of oscillation to take the decision of apoptosis or cell survival. P53DINP1, which is the mediator of this feedback, is added as a variable to a 2-D oscillator model of the p53 network. The resulting canonical 3-D model successfully replicates the two-phase dynamics. That is, it possesses temporary oscillatory behavior, in which first oscillations (first phase) and then high level state (second phase) are observed. By introducing a new variable to the core oscillator in the p53 network, this study demonstrates that p53 network can be considered a modular structure, which consists of an oscillator and other variables that control this oscillator to contribute to cell fate determination.