[Dance] Argentine Tango group class

I started going to an Argentine Tango group class at Starlite. At first, I was not sure how to lead the Cruzada. Cruzada means "crossed"; in this case, Cruzada refers to the position of the legs. I was not sure how my partner was supposed to physically feel when doing this move. The correct way of leading the Cruzada is when the follower's right foot touches the floor, the leader should push her with his right forearm toward the left. This "push" is actually a pulse instead of a continuous push. Also, my parm is on her back, so I can't use my hand to lead this move.
Then, we learned the Cadencia. The Cadencia seemed similar to the Tango Rocks in the American Tango. The teacher said we can put the Cadencia anytime, anywhere.
Tonight's routine went like this:
1. Move to the left with the left foot.
2. Move forward diagonally to the left with the right foot.
3. Move forward diagonally to the left with the left foot. The follower moves her right foot backward. When her right foot touches the floor, push her to the left with the right forearm.
4. Move the right foot close to the left foot. The follower crosses her left foot in front of her right foot. This is the Cruzada.
5. Pivot on the right foot to the left a little.
6. Move backward with the left foot.
7. Pivot on the left foot to the right. Now, the follower is on the left.
8. Move backward with the right foot.
9. Pivot on the right foot to the left.
There were two options from here:
10. Move forward with the left foot
11. Move to the right with the right foot.
12. Move the left foot close to the right foot.
Or:
10. Repeat from step 1.

A Guide to Tango Terminology