reflexives - "Themselves" or "Themself" in a singular context?

I have the following sentence:

In order to read the remainder of this book, the reader is advised to familiarize themselves with the concepts contained within this Chapter.

I want to put:

In order to read the remainder of this book, the reader is advised to familiarize themself with the concepts contained within this Chapter.

In this very great article here, it explains why you should use themself only in an informal context, and the sentence they gave supports this, however; In the sentence I have, it sounds plain wrong (as sometimes proper English tends to sound, admittedly), despite what they say. Should I still use themselves, because it is in a proper context, or am I able to use themself instead, despite its proper context?

Answer

The singular "they" and its spawn are notoriously frustrating and controversial. Because your question is about what you "should" do, I would suggest a reasonable workaround:

In order to read the remainder of this book, the reader is advised to become familiar with the concepts contained within this Chapter.

I believe your understanding of what is acceptable, in terms of the reflexive pronoun, is correct. However, in most cases it is relatively easy to sidestep the conundrum altogether.