Select vertices by proximity to transform mesh

Hello!

I'm a beginner and this is my first post. I am trying to select the vertices of a mesh by their proximity in order to move them and, as a result, transform the mesh. I've created this model as an exercise as I continue learning Grasshopper. Thanks to anyone that can offer guidance.

I've combed posts and tutorials, and have tried many different components but I haven't had luck solving this. I understand the Proximity 3D component has an output (T) that "outputs for every point in the set a list of integers. These integers are the indices of the points that were connected. So this basically allows you to figure out which points were close", but I couldn't figure out how to make use of the data plugging in List Item to select existing points, so I reverted to End Points from the Links as Tree output. I'm also not able to solve how it feeds back to transform the mesh. Could I use Hoopsnake to auto update moved vertices?

1st technique goal

Select the vertices of a mesh by their closest proximity in order to move them and, as a result, transform the mesh

2nd technique goal

Is it possible to select vertices of a mesh by a defined range for proximity? For example, can I select only vertices that are more than a given distance from one another but less than a second greater distance from one another?