synonym of "to-do" in English

It depends what context you are using it in.  

Can you use it in a sentence so we know how you are using it?

As an element of table of content;
As;
1. Introduction
2. TODO (but what should I write for this?)

Kind regards.

So, as a chapter in a book??

Yes, or in a thesis, but the meaning should be like that and must formal heading.

To rephrase, what is the formal saying of to do?

Regards.

perform the act of

Actions required

Is the phrase being used to communicate that the content of the chapter is helping the reader with his/her own to-do's, or the author's "to-do's", is it even about action-items in that sense at all?

Proceed with

to-do can be regarded as a noun.
It was developed when people made lists of tasks to do in the near future.
Eventually those lists were called to-do lists. The name has taken on a life of its own as a noun.
some synonyms have already been listed. The most appropriate one would be
tasks

Tasks leftover
or Actions left?

I need to have something to replace that "left".

Kind regards.