assuage, verb. To ease or soften something painful. Etymonline characterises its typical objects as pain, anger, passion or grief, and that list is the useful part of the entry.
Notice what it never seems to take. You assuage guilt, fear, hunger, doubt, a conscience. I can't think of a sentence where someone assuages delight, and I don't think I've ever seen one. The verb appears to need something bitter to work on.
The root explains why. It reaches English around 1300 as asswagen, from Old French assoagier, from Vulgar Latin adsuaviare, built on Latin suavis, sweet or agreeable. To assuage grief is, at the bottom of the word, to sweeten it.
That is the whole shape of the thing. It presupposes a sour taste and adds sugar. Which is also why "assuage" always feels partial to me when I read it, in a way "cure" or "end" does not. Sweetening is not removing. The grief is still grief; something has been added to make it bearable.
The cousin worth knowing is suave. Same suavis, same PIE root swād-, sweet or pleasant. And sweet itself comes down from that root too, through Germanic rather than Latin, so English ended up with the same ancient idea arriving twice by different doors and settling into completely different registers. One is a taste, one is a manner, one is what you do to someone's fear.
Middle English also had a clipped version, swage, which I would quite like back.