How do I view an array that is inside of an array in the unity inspector?

Hey, so I'm working on some NPC logic for my game, and I have a simple dialogue system in place. I want to expand on it by having the NPC say something else in its dialogue each time the player talks to the NPC.
Basically what I am trying to do is this:
First time the player talks to NPC: NPC gives the player a quest and says some other things, you get the point.
Second time: If the player has not completed the quest, I want the NPC to say something along the lines of go and complete the quest.
Third time: If the player still hasn't completed the quest, say the same thing as the second time.
Fourth time: If the player has completed the quest, say something different like congratulations and something like that.
So what I tried to do to implement this was to have a Dialogue class that just contained a string array of sentences. Then what I did was in my NPC script, I made an array of the dialogue class like so:
public Dialogue[] dialogue;
The problem I have is that when I add an element to the Dialogue array in the inspector, the string array I made in the Dialogue class does not show up in there. The class did have
[System.Serializable]
on top of it so I don't know what would be doing that. I'm also not entirely sure how to add this to my dialogue system. If anyone knows how to do this, please help.