Word similar to guarantee

I’m not looking for a synonym and I’m not sure what the word is for this. There are comparatives and superlatives for adjectives but I’m looking for a verb. A guarantee, assurance, or promise imply 100% likelihood of something happening (obviously this isn’t how it works in real life, I’m sticking strictly to definitions). I want a verb that is to a lesser degree than these terms.

For example instead of saying “I can guarantee your satisfaction.” I want to say “I can your satisfaction.”

I’ve thought about this but there are only phrases such as “I promise I will try my best” or “you have my word”. A nice short verb would be preferable