What's the best order to do this in ?

My lawn just got its late summer. early autumn feed a week or so ago, now I
plan to scarify, hollow tine aerate and then top dress it before winter sets
in.

My current plan is to wait for a couple more rainy days so that the
fertiliser is all intot he soil, then cut it as low as possible, scarify it,
then hollow tines aerate it. The guy that does the HTA wants to leave the
corings on the lawn to break down naturally, so I presume I need to wait for
a few more rainfalls to break then down, then go ahead with the top
dressing.

Does this sound about right, or would anyone recommend a different approach
?