openstreetmap - Listing churches with their administrative location using Overpass

I'd like to extract a list of churches from OSM with their name, their coordinates and the name of the lower administrative division they belong to. I managed to get the first ones with:

area["name"="Mayenne"]->.boundaryarea;
way(area.boundaryarea)["building"="church"];
out tags center;

I deliberately ignore nodes and relations as they don't seem relevant in this case.

I can't find a way to retrieve the name of the lower administrative division. Is there a way to do it?