According to Piaget's cognitive development theory, when the learner…

In Piaget's theory of cognitive development, the mind builds understanding through two complementary processes: assimilation, where new experiences are fitted into existing mental schemas, and accommodation, where existing schemas are modified to fit new experiences. Equilibration is the higher-order, self-regulatory process that coordinates assimilation and accommodation so the learner maintains a stable balance between their internal cognitive structures and the demands of the external environment; it is this process that drives the learner from a state of cognitive imbalance (disequilibrium) back to equilibrium and, over time, propels development to more advanced stages.

The question describes exactly this coordinating, balance-maintaining process — a learner keeping a proper balance between themselves and their environment — rather than either of the two component sub-processes alone. That overarching balancing mechanism is what Piaget named equilibration.

• Accommodation covers only modifying an existing schema to fit new information; it is one of the two component processes that equilibration balances, not the overarching balancing mechanism itself.

• Assimilation covers only fitting new information into an existing schema without changing it; it too is a single component process, not the overall self-regulatory balance described in the question.

• Integration is not a term Piaget used for this cognitive-balancing mechanism; it does not correspond to any process defined in his theory.

Hence, the mechanism by which the learner maintains a proper balance between themselves and their environment is Equilibration.