Deep learning models have become increasingly computationally intensive, requiring extensive computational resources and time for both training and inference. A significant contributing factor to this challenge is the uniform computational effort expended on each input example, regardless of its complexity. We introduce \textbf{DynaLay}, an alternative architecture that features a decision-making agent to adaptively select the most suitable layers for processing each input, thereby endowing the model with a remarkable level of introspection. DynaLay reevaluates more complex inputs during inference, adjusting the computational effort to optimize both performance and efficiency. The core of the system is a main model equipped with Fixed-Point Iterative (FPI) layers, capable of accurately approximating complex functions, paired with an agent that chooses these layers or a direct action based on the introspection of the models inner state. The model invests more time in processing harder examples, while minimal computation is required for easier ones. This introspective approach is a step toward developing deep learning models that ``think'' and ``ponder'', rather than ``ballistically'' produce answers. Our experiments demonstrate that DynaLay achieves accuracy comparable to conventional deep models while significantly reducing computational demands.