Reliably means “in a way you can trust, again and again.” If a bus runs reliably, you can plan your morning on it. If a friend shows up reliably, you are not guessing whether they will come. If a machine or a test works reliably, you get a steady result, not a wild new answer each time. The person or thing is reliable; they act reliably — one word names what they are, the other names how they behave. You hear it a lot with services, tools, memory, and people who do not let you down. Though actually, I can reliably say is a grown-up, slightly careful way of saying “I am quite sure,” as if your knowledge itself can be depended on. That is a stretch from buses and friends to the speaker’s own claim.