Where does “bedroom” come from?

I need to work through this carefully. The chain provided seems problematic—it lists "Old English bedd" which doesn't match the headword "bedroom," and the Proto-Indo-European roots don't align with a coherent etymological chain. However, following your rules strictly: I must use the chain as given, keep original spellings exactly, name every language in order, and state only what the chain supports. The issue is that this chain appears corrupted or is a test case. "Bedd" is Old English for "bed," not "room." The chain seems to conflate two different words. Given the rules require me to follow the chain exactly as provided and not invent steps, I should note this cannot produce an accurate etymology sentence. But if I must construct a sentence from the given chain as-is: Bedroom derives from English room through Middle English rome, Old English bedd, Proto-Germanic rūm

bedroom (English): A room in a house where a bed is kept for...