Research: Adelaide is researching (on the down low) spirits, possession, and the sliding scale of spirit to demon and if there's a way to reverse the process once a spirit is tainted. More overtly she's researching the shards and their effect on the rifts- as it's very new there isn't anything in writing about it but any accounts she can find about what happened with the herald would be in her area of interest.

Experimentation:

SO I was wondering if she couldn't, in light of members of the inquisition going missing and others getting kidnapped, put in the research and experiment with making something that is similar to but not quite a phylactery. A little blood in a pendant that'll glow in time with the person in question's heartbeat when a phrase is uttered and can be used with a map via pendant scrying to give a general 'that a way' idea of where the person is. Since she's working from the ground up it'd take a lot of time, effort, and work to figure out how to create it and since it's Adelaide she'd only manage the one with her own blood in testing before she attempted to pitch it to anyone.