Although both words can be found in dictionaries, I'm constantly forgetting which one is which.
Are there any mnemonic rules that would help me remembering them?
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You have a regular spelling in loose, adjective, and a special spelling in to lose, verb. I would say the drop of one o is an optical help to distinguish the two words.
As a mnemonic help you can arrange alphabetically:
A adjective loose with Ŕegular spelling
V verb lose with Śpecial spelling.
Try if this helps. If not, you have to invent something better. I did such things sometimes with my pupils to improve their creativeness to invent memory aids on their own.