I am trying to say something like "The button labeled 'blue' at the lower right is red."
I know that adjectives can be connected together with their て-form. It seems like maybe the the same should happen with verbs, but the ordering and sentence connection implied by the て-form makes this sound awkward to me. For some reason, I also cannot find examples on this.
The two verbs I am thinking of are ある and 付けられる (labeled?).
My current translation is 右下にあって「blue」と付けられたボタンは赤いです。
May someone explain how to connect with multiple noun-modifying verbs? Also, what is a natural translation for my example sentence?