nothing is showing up in my XSL Output screen. No parsing errors, just
a blank screen.
If nothing shows up in the output, then the problem is not with sorting. Your stylesheet, when applied to your input, should produce the following result:
<?xml version="1.0"?>
<assembly>testtesttesttest</assembly>
This may not be the result you expect - but it is not blank, so look for the error in how you initiate the transformation, before polishing your stylesheet.
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BTW, although it's difficult to see, those 4 test strings in the result ARE sorted by the name attribute of the parent string.