On the second strike you automatically gain ADV due to the Weaponmastery property of the Dart, so you can use your Bonus action to cast hunters mark and gain an additional d6 DMG that turn for a final of, 2d10 fire, 2d6 psychic, 1d6+1d8 force, 1d4+5 piercing and pray to the gods you don't crit.."
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He's a veteran player with extensive knowledge of 5e, so I assumed he had interpreted it correctly.