Trailblazer's Torch

Only one player can have the initiative at a time. As one player takes the initiative, any other player that had the initiative ceases to have it.

There is no initiative in a game until an effect instructs a player to take the initiative. Once a player is instructed to do this, they have the initiative until another player takes the initiative.

If you're already in a dungeon when instructed to venture into Undercity, you move to the next room of that dungeon. If you are already in the last room, you will complete that dungeon and start Undercity. This is true whether you're already in Undercity or any other dungeon.