Define "complex adaptation." How do we distinguish a sufficently complex adaptation from a non-complex one for the purposes of your criteria?
Secondly, what qualifies as a random mutation? Does retrovirus infection count? UV damage? Changes in ploidy? Or only errors in replication? Normal sexual recombination is random to a certain extent. Does that not qualify? Why not?
"How do we distinguish a sufficently complex adaptation from a non-complex one for the purposes of your criteria?"
Most adaptations are complex. There are a few that aren't, mostly that only require changes within one gene of only a few amino acids.
"what qualifies as a random mutation?"
Anything that is not organism-directed (either the organism itself or other organisms).
"Does retrovirus infection count?"
Nope.
"UV damage?"
Yes.
"Changes in ploidy?"
This has not been sufficiently determined. I would lean towards "no".
"Or only errors in replication?"
Interestingly, I'm pretty sure much of what is considered "errors in replication" are processes we simply don't understand.
"Normal sexual recombination is random to a certain extent."
Are you sure about that? I would ssay that the only thing "random" about it is that we don't understand the process.