Reduce Avatar Progress

The progression of the avatar project is "collected" in the "alien facility" sites which look like this on the global map:

When you successfully attack such a facility, the aliens lose the progress from that facility and they have to build a new one in a different region. As you can see by the red square below it, the facility in this screenshot has only collected one point yet, so it is not yet a priority. But before you can attack a facility, you have to establish contact with the local resistance of the region. This isn't done with the region of this facility yet, so I should better do that soon so I can take out that facility quickly when the aliens get close to completion.

The facility in the pacific ocean which you see as soon as you become aware of the avatar project can not be attacked (yet!). It represents any project progress which is not bound to a specific facility.

Avatar progress can also be reduced by events which will happen when you progress in the "Alien Blacksite" and "Codex" story arcs.

You can attack a facility in a region you have not contacted, given the correct circumstances. This requires you to acquire a "mission lead to alien facility" or whatever it's called. This can be gotten at least from a hack reward or sometimes you can buy it from Black Market.

Then you have to research it. It's a quick research but it also takes some intel to do so. After the research it is possible that it does not reveal a new facility on the map, but instead "gives you the exact coordinates" for a facility of which whereabouts you already knew about but did not attack due to not having contact in the corresponding region.

If that happens, you can actually fly over there and attack the place even with no contact. Or you can click its button on the bottom of the screen in the geoscape view (you can also see from the looks of the icon that it's unlocked now). I guess the flavor is such that when you researched the coordinates, you no longer need the local resistance to inform about the exact location of the facility.

I had this happen to me two days ago. I had an alien facility in Australia but I had no contact there. I previously had gotten a facility lead from a hack reward and decided to research it because avatar progress was almost maxed out. When it finished, I was disappointed because it only "revealed" the site in Australia I already knew about. I thought I wasted the intel, but on closer inspection I noticed its icon had changed (I had another unreachable alien facility next to it), and I was able to fly there and give it an X-4 treatment.