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In Piaget's theory of cognitive development, reversibility is the cognitive ability to recognize that actions can be reversed, leading to the original state or condition. This concept is primarily developed during the concrete operational stage, which typically occurs between the ages of 7 and 11 years.

Symbolism is an essential aspect of cognitive growth that occurs earlier in the preoperational stage. It involves the use of symbols, such as words and images, to represent objects or concepts that are not physically present. For children to understand reversibility, they need to be able to mentally represent actions and the objects they change. This ability to create symbolic representations supports the understanding that operations can be undone, making it a necessary prerequisite for the development of reversibility.

The other options, while important in other contexts of cognitive development, do not specifically establish the foundation necessary for understanding reversibility. For instance, self-awareness pertains more to an individual's understanding of themselves and their identity, while meta-cognition involves thinking about one's own thinking processes. Hypothetico-deductive reasoning is a higher-level cognitive process associated with the formal operational stage rather than the concrete operational stage where reversibility is typically mastered.