Shadow Step: At 6th level, you gain the ability to step from one shadow into another. When you are in dim light or darkness, as a bonus action you can teleport up to 60 feet to an unoccupied space you can see that is also in dim light or darkness. You then have advantage on the first melee attack you make before the end of the turn.

Cloak of Shadows: By 11th level, you have learned to become one with the shadows. When you are in an area of dim light or darkness, you can use your action to become invisible. You remain invisible until you make an attack, cast a spell, or are in an area of bright light.

My question is does using shadow step end the invisibility of cloak of shadows? CoS reads the same as the invisibility spell, only ending by using the attack action or casting a spell, but the way shadow step is worded it seems like it's neither an attack nor a spell. By comparison, the spells granted by shadow arts (silence, dakness etc.) are described as being "cast", and so would end CoS.

So can I stay invisible while I teleport, or is that all sorts of broken?