Please Explain Influence and Borders

Or... How can I subvert that alien planet that is in the middle of my territory?

So early in the game, a rouge alien colony ship snuck in an colinized a Class 4 planet (refered to as mars from now on) right next to my home world. How to I convince these aliens that they would be better off under my rule?

Is the answer:

Embasies on a planet near Mars?
Influence bases near Mars?
Overall influence across the universe?
More importantly, how do I tell if any of my efforts are having an effect? Trade (either with ships, or via the "speak to" screen)

Or do I just have to blast 'em?
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