So I did/I did so

[joham]

I thought I ought to do my homework first. And So I did/I did so.

Are both phrase fine with the first sentence? Thank you in advance.

[RonBee]

I thought I ought to do my homework first. And So I did/I did so.

Are both phrases fine with the first sentence? Thank you in advance.

Not to me. I would only use And so I did.

[joham]

Thank you so much, moderator. And how about:

The doctor told him to breathe deeply, and so he did/he did so.

And how should we decide which to use?

Thank you again.

[5jj]

The doctor told him to breathe deeply, and so he did/he did so.

More likely: and so he did - and, as a result of the doctor's instruction, he breathed deeply.
Possible: and he did so - and he did what the doctor had instructed him to do - breathed deeply. The 'so' is not essential here.