Given a fantasy world in which magic exists and which dragons are real, what kind of tactical advantages could a dragon and rider pair have over dragons without riders?
To expand on the setting:
Dragons are sentient beings with intelligence and personality equal to or greater than that of humanoids. They have their own natural methods of performing magic inaccessible to non-dragons, and some dragons can expand their understanding of magic through study. They have the ability to shape shift (with considerable mental effort) into any natural shape, most often a humanoid form to ease social interaction or provide access to human spaces. They range in size depending on age, though usually only younger ones have riders and they can not normally carry more than one or two people at most. They live five to ten times longer than humanoids, with adolescence starting around one hundred years of age and most retreating to isolated family lairs by adulthood around age three hundred. Their scales are hard, but are still natural material, so metal weapons can pierce them and armor can still benefit them, though the burden is undesirable in most cases. While their digits are dexterous enough to manipulate objects, they are unlikely to wield weapons themselves. They can breathe either fire, lightning, ice, poison, or acid depending on their race, though volume and frequency is dependent on age. Riding harnesses/saddles exist as well.
Humanoids that ride dragons are fully sentient and intelligent, capable of performing magic with enough training. There is a wide range of cultures ranging from bronze age through renaissance depending on the nation. Simple clockwork exists in some areas and alchemy is an emerging science in the world.
There are also other sentient and intelligent creatures capable of magic in the world, but dragons and humanoids are the primary inhabitants.
There are no chemically propelled missile weapons.
So far, I have settled on that a dragon with a rider has the following advantages:
A second set of eyes: The dragon rider is able to keep an eye out on spots that dragons normally can't see as well, including above and behind. Dragons being apex predators are not normally inclined to look above or behind them when in flight and this is the primary method of attack during dragon on dragon combat.
In flight first aid: Most dragon riders are trained to bandage and use quick healing magic to patch up their dragon while still in the air.
Close combat support: Dragon riders can use pole arms like lances and glaives to great effect from dragon back. They can also train to use archery from dragon back. While not as effective as the dragon itself, they still add some force, provide the opportunity to attack other dragons from below, as well as deter other dragons or people trying to drop on or flank the dragon.
Mobile magic might: A rider experienced in magic can use the vantage point provided by the dragon to safely cast magic with little worry of being interrupted. If the dragon and mage have practiced at length, the mage can even access the magical power available naturally to the dragon.
Communication: Using signal flags, friendly riders can communicate while their dragons focus on staying aloft. This allows for more effective tactical coordination.
So what I am looking for now is what other possible tactical advantages could a rider provide to a dragon during either mass or single combat? Additionally, if there are any tactics that humanoids could employ against dragons beyond simply brute force efforts like hails of arrows or really large fireballs, those would also be appreciated (I have read a number of other answers to the 'How to fight dragons' question, but none seemed particularly fitting).
(PS, this is my first question on here, so please let me know how I can improve it if you see anything missing.)