Is this the correct form ?
I would love to do this as soon as you will do that.
Or is it
I would love to do this as soon as you have done that
Or is there a better way to form this sentence ?
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I think this matter is being unduly complicated by the use of 'this' and 'that'. For they have usage rules which are separate to your main point about the tense of the second 'do'. So let's just remove 'this' and 'that' for a moment and insert some specific things. As I see it your dilemma is over whether to say:
'I would love to go to New York, as soon as you will find a job.'
'I would love to go to New York, as soon as you have found a job'
The second example is now perfect. The first would be correct grammar if you removed the 'will' i.e. 'as soon as you find a job'.
However, I prefer the second.
Use of 'this' and 'that' is a wider discussion.