Sometimes you nee3d to return to space for those quests to update.
Please note that sometimes a quest-specific strike is added to the planetary map and that is the one you must select; it will appear next to the "normal" strike icon on the planet map and that is how you complete the quest step.
I hope this helps!
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Thanks - the flashing icon on the Patrol waypoint was for an entirely different quest - a fireteam based objective. The actual Promethean Code quest was located at a dedicated waypoint that I completely overlooked. Coupled with the "incomplete" quest log I was really confused, but problem solved now!
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Good Luck Guardian!