Numerical methods, the Ronge-Kut method for the Bootcher system 6 order

It is necessary to add animation to the low-poly main character and give him the ability to hold a weapon (tool) that will aim at the cursor. The game is from a third-person perspective, with the camera behind the player and the cursor in the center of the screen. The character needs to be able to enter aim mode, the camera slightly zooms in, and the character should be able to use the tool (a laser tool for resource gathering). I have a ready animation controller from Synty - Third Person Controller. It can be used or the animation can be completely set up from scratch if that is easier. In the end, I expect a character that can select a tool (one large two-handed and two small ones), switch tools, aim, and have the head and the tool look at the point where the cursor is pointing.