"Basieren" doesn't work here?
The only way you can use "basieren" is "auf etwas basieren" (to be based upon something / based on something) e.g. "Die Geschichte basiert auf Fakten" (The story is based on facts)
Thank you. The distinction makes sense.
Duden gives a second meaning 'to found' ("Wir haben unsere Pläne darauf basiert") but I wouldn't bother about it at all. It's very rare. I have never heard it been used in that sense.
Thanks. That's good to know. I read (or perhaps I should say "very slowly make my way through as well as I am able") some older texts in German, so it could show up.