<s>[INST] Given that two unit circles are tangent externally to a larger circle which is a unit circle raised two units on the y-axis. This means the center of the larger circle is at (0, 2), with a radius of 2 units. Draw the circles, suppose we put a small ball in the space between the unit circles and larger circle, and slightly nudges the ball in the tangency point of the unit circle closest upwards. What is the path the ball will take as it rolls around a comple after it leaves the larger circle in that same tangent point?[/INST]