AI that builds a tower

I am looking into building an AI that:
-Receives a task from a visual list of tasks (like stickies on a white board)
-Builds an object based on task received
-Carries the object to a stack of previously built objects
-Stacks the new one on top making a sort of tower

The stack would be say, 3x3 so once all 9 objects make up the first layer, the AI would start stacking on the 2nd layer, etc. It could go very high. I was thinking about building a sort of scaffolding or stairwell on one side of the tower that the AI would climb.

I am just not sure exactly where to start. Most specifically - how do I make an AI that picks something up and stacks it in a grid? Should each stackable object have a bone and a socket? It would need to have physics off, too probably so nothing falls over? What are some blueprint nodes to look into? Also how do I make an AI pick up an object and carry it? I would attach the object temporarily to the AI carry animation in the state machine or in the behavior tree?

Thanks so much for any feedback!!