What is agile and how does it integrate with a PM methodology?

Continuing with posts on agile, what is agile and how does it integrate with a project management methodology?
Often, we see posts about “Agile Project Management” or “Agile Methodology” and these things do not exist.
We also read about the #Agile_Mindset, #Agile_Approach, #Agile_Framework, … Values, Principles, etc. Yet, what do these things mean?
Often, practitioners fail to see that Agile and its various linked models like #Scrum, #Kanban, etc. are mostly about development life cycle or the development phase of a BUSINESS project. In other words, projects must start with the concept, feasibility, business requirements, before we reach the stages of design and development. The following image presents this concept.

The cycle before the close stage is the development life cycle where Agile Values, Principles, Framework can be used on a given project. The rest of the work follows sequential (but possibly overlapping) stages from idea to closure.
What is also interesting to us is the concept in the following image:

The point in this graphic is that one of the selling points we keep hearing about agile is customer engagement. One of the annoying things about this point is that it is often made by Agilists with the indirect presumption/claim that customer engagement is not present in traditional project management, which is, of course, a faulty presumption.
The second part, which we think is the flaw highlighted in the graphical box above. Most Agile references and even now the PMBOK Guide continue to stress that the discovery phase (concept – feasibility – business stages) are outside the project life cycle. Basically, the point stressed by these references is that period is the responsibility of the business and not project management. To us, that is not logical because these folks miss the point that the project success and failure is pre-set with the business side during the discovery phase. If the customer defines the project without input and direct involvement of project management then something will be missed and will often lead to costly rework if not project failure.
Therefore,

1. Successful project management and product delivery must follow a project life cycle or a stage-gate process.
2. Successful product (and project) starts with the proper ideation, concept, and feasibility study, the Discovery Phase in CAMMP™ (The Customizable and Adaptable Methodology for Managing Projects™).
3. Successful product (and project) delivery depend on an integrated team approach where the customer, project management team, and development team works collaboratively; across all stages of the project.

For more about the CAMMP™ Principles and Critical Success Factors, refer to the next image.

What are your thoughts?