Recently, I was asked how to improve the quality of a software written by other people a couple of years ago. I was informed that it was working, the only missing thing was compliance to software development procedures. I recommended to do the above sequence in reverse, i.e. first planning and executing full system tests. That way, we can answer the most important question, "is it working correctly". After we are satisfied with the tests, we can review and document the design and refactor code.
Even if we have to stop after testing, we will have added value to the existing product by being able to demonstrate in a repeatable manner that it is working. If we started the development sequence from the beginning and had to stop midway due to other priorities (which always happens), we would have wasted our time.