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so, the olympian's trial are all rng from exploration, so i can't help with this one

geography of northeastern myths is easy, just gotta got to the non-fiction section of the hinterlands library

epinikion is a reward for finishing khembish's hangout scenes, so just ask jean for a cook and spend time with the boar boy. 

the torn illustrated page i don't know,, unlike the epinikion i can't use the context clues of it's description, could be a random reward from the valley, like most mementos. maybe it's a reward for finishing asterion's project. but i could be wrong and it be something else entirely

I'll see what I can do. Thanks for your help