Are there any forms of divination in Harry Potter that truly work, besides prophecies by Seers?

In Harry Potter we know of at least one form of divination which is real and can make true predictions about the future, namely special prophecies made by true Seers. However, other forms of predicting the future are introduced, specifically the methods of the Centaurs, and the various techniques taught by Professor Trelawney.

Is there any indication in canon or the usual sources (Rowling, Pottermore, etc.) that any of these other forms of telling the future truly work?

The books seem to suggest that Centaurs can, in some instances, with little precision and only after years of training, glean some understanding of the future from the movement of stars. However, it is constantly repeated that such divination is extremely difficult, never precise, and that often even the best will misinterpret or make mistakes. It seems to me that the books never clarify whether the future is truly written in the stars, or if the Centaurs' divination is simply a sort of folk spirituality.

This question is motivated by two specific instances in the books. Firstly, when Harry and Hermione are doing detention with Hagrid in the Forbidden Forest in the first book they run into the centaurs Ronan and Bane. Both comment on the unusual brightness of Mars. Later in book five Firenze explains in one of his lessons that

"In the past decade, the indications have been that wizardkind is living through nothing more than a brief calm between two wars. Mars, bringer of battle, shines brightly above us, suggesting that the fight must soon break out again. How soon, centaurs may attempt to divine by the burning of certain herbs and leaves."

This, as far as I know, is the only instance in the books of a correlation between the Centaurs predictions and actual events.

The second instance comes in book six, around Christmas, when Harry rushes to go to one of Dumbledore's private lessons.

"Harry proceeded through deserted corridors, though he had to step hastily behind a statue when Professor Trelawney appeared around a corner, muttering to herself as she shuffled a pack of dirty-looking playing cards, reading them as she walked. “Two of spades: conflict,” she murmured, as she passed the place
where Harry crouched, hidden. “Seven of spades: an ill omen. Ten of spades: violence. Knave of spades: a dark young man, possibly troubled, one who dislikes the questioner —” She stopped dead, right on the other side of Harry’s statue. “Well, that can’t be right,” she said, annoyed, and Harry heard her reshuffling vigorously as she set off again, leaving nothing but a whiff of cooking sherry behind her.

Ever since Harry, Ron, and Hermione first sat in Professor Trelawney's classes the books have made it clear that the various methods Trelawney teaches have no predictive power. Even Dumbledore makes it clear at the end of book three that this is his view when he says to Harry:

"Do you know, Harry, I think she might have been," he said thoughtfully. "Who'd have thought it? That brings her total of real predictions up to two. I should offer her a pay rise...."

So I was very surprised by the passage above. Trelawney seems to be making her usual grave and general predictions: conflict, and ill-omen, and violence. Then she suddenly describes in fair detail and specificity, with perfect accuracy, the scene we are watching as viewers: "A dark young man, possibly troubled, one who dislikes the questioner." All (we are led to believe) from drawing a card!

Sorry about the long question. This has been nagging at me for a while, I'm very curious to see what people think!