No reason to stop at print("print()"), you can nest further, print('print("print()")'). And then you can short-circuit the process, write a single program which first does print(), then print("print()"), then print('print("print()")'), then the next level, then the next level, etc. And no need to stop there: once you have that program, you can print IT. And then continue the process.

I've done this up to level omega^omega at my Library of Intuitive Ordinal Notations: https://github.com/semitrivial/ions/