Crossword Genius

Doctor meets a patient inhaling oxygen slowly (3,4,2,1,4)

Ross

I believe the answer is:

one step at a time

I'm a little stuck... Click here to teach me more about this clue!

'patient inhaling oxygen slowly' is the definition.
I know nothing about this answer so I can't tell whether this works.

'doctor meets a' is the wordplay.
I cannot really see how this works, but
'doctor' could be 'me' and 'me' is found in the answer.
'a' could be 'one' and 'one' is present in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for one step at a time that I've seen before include "without rushing" , "Gradually" .)

I've seen this clue in The Hindu.
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