The PMBOK's full name is "Guide to the Project Management Body of Knowledge". It isn't designed to tell you what to do, but it is a way of organizing the breadth of knowledge that is likely to be useful and relevant to someone working in the field of project management.
The most relevant process group would be the Monitoring and Controlling Process Group. These are the set of processes that are about reviewing the performance of the project and updating the plan as necessary, including monitoring and controlling work, performing change control, controlling scope, controlling schedule, monitoring risks, communicating, and managing stakeholders.
The most relevant knowledge areas would be Project Scope Management, Project Schedule Management, Project Risk Management, Project Stakeholder Management, and Project Communication Management.
What you do would be define in your project plans. There are different ways to organize planning information, but early in the effort you should have considered how you will manage scope, schedules, and risks. When the project meets thresholds, you will need to communicate with stakeholders to inform them of the health and status of the project, which would have been defined in some kind of communication or stakeholder management plan. If you had a specific contract with a client, these plans would tend to be agreed to by both parties as part of contract negotiation or project planning.