A proof that ought implies can

Some actions are are things I can do immediately: for instance, I can immediately raise my hand. Others require that I do something to enable myself to do the action: for instance, to teach in person, I have to go to the classroom, or to feed my children, I need to obtain food. So, here is a very plausible axiom of deontic logic:

1. If I ought to do A, and A is not an action I can do immediately, then I ought to bring it about that I can immediately do A.

Now, say that I remotely can do an action provided that I can immediately do it, or I can immediately bring it about that I can immediately do it, or I can immediately bring it about that I can immediately bring it about that I can immediately do it, or ….

It follows from (1) and a bit of reasoning that:

2. If I ought to do A, then I remotely can do A, or I have an infinite regress of prerequisite obligations.

But:

3. It is false that I have an infinite regress of prerequisite obligations.

So:

4. If I ought to do A, then I remotely can do A.

'Ought' implies 'can'?

I am sick. Here's a heartening argument: Next week I have some teaching and I can't teach while sick. I ought to do the teaching. Ought implies can. So I will be well by next week.

One gap in the argument is that my doctor may tell me I'm not sufficiently infectious to be unable to teach. But that can't be all that's wrong with the argument.