Final answer:
The next action a project manager can take to close out a project successfully is to reassess and potentially adjust the project scope and deadline based on the additional tasks added by stakeholders.
Step-by-step explanation:
In this situation, the next action a project manager can take to successfully close out the project is to reassess and potentially adjust the project scope and deadline.
The project manager should communicate with the stakeholders to understand the additional tasks they are adding and evaluate the impact on the project scope and deadline.
Based on this assessment, the project manager can then make informed decisions about whether to negotiate new deadlines, reallocate resources, or adjust the project scope to accommodate the stakeholders' tasks while still achieving a successful project closure.