Before players there is a task to enter the tower alone and climb on 50 floors, which are becoming increasingly harder with various enemies and waiting tests. If you die or you will end time, you will have a chance to make another attempt.
You also have the opportunity to come and leave, considering the fact that there is no daily limit or mechanics of charging.
You will need to fill in Public Ads Tower Advancer in Quests, before you go to any densely populated central city and look for a tower symbol on your map.
As soon as you interact with the tower, you will be prompted to choose which tower you would like to clean and what floor.
Remember that this occupation can only be performed by you, so make sure you have good equipment and engraving before accepting a challenge.
To learn more about Lost Ark, check out the section What is a cube in Lost Ark? in professional guidelines for the game.