The Managing Product Delivery process in PRINCE2 links the Project Manager and Team Manager roles.
This connection is crucial as the Project Manager assigns work to the Team Manager, who is responsible for the production of the project's products, ensuring that the work is done to the right quality, at the right time, and within cost constraints. References: PRINCE2 Foundation manual, PRINCE2 official resources

The purpose of the Controlling a Stage process in PRINCE2 is to monitor and control a stage by managing work progress, assessing issues and risks, and ensuring that deviations from the plan are identified and managed within tolerance. It includes taking corrective actions when necessary to keep the project on track.
References: PRINCE2 Foundation manual, PRINCE2 official resources

According to PRINCE2, a project should have tolerances defined for each project objective. Tolerances specify the permissible deviations in scope, time, cost, quality, risk, and benefits that are allowed before the deviation needs to be escalated to a higher authority. This is fundamental for the 'manage by exception' principle, allowing efficient use of time and resources by project management levels.
PRINCE2 Foundation Manual

A minimum requirement for applying the Change Theme in PRINCE2 is to record every issue that is raised in the issue register. This ensures that all potential and actual deviations from the plan are captured and managed appropriately, maintaining control over changes and supporting effective decision-making. References:
PRINCE2 7 Foundation Handbook and official training materials.

The 'Implement' step within the recommended risk management procedure in PRINCE2 involves taking planned actions to respond to a risk. This step is crucial as it moves the risk response from the planning stage into actual execution, thus addressing the risk directly to mitigate its impact on the project.
PRINCE2 7 Foundation study guide and official documents.