What process group establishes project scope, refines objectives, and defines the actions necessary to attain project objectives?

The Executing process group directs and manages the performance of the work defined in the project management plan - it does not establish scope or define actions.

The Planning process group encompasses all processes required to establish the project's total scope of effort, refine its objectives, and develop the project management plan and project documents that will guide execution. This includes defining schedule, cost, quality, resources, and risk - all of which translate objectives into an actionable roadmap. PMBOK explicitly defines this as the purpose of the Planning process group.

The Initiating process group authorizes a project or phase and defines it at a high level, but does not refine objectives or define the full set of actions required.

The Monitoring and Controlling process group tracks, reviews, and regulates project progress against the plan - it does not establish scope or define new actions.