As ad asol, your goal is to scale into the most optimal full build possible. In order to stall, you must go for muramana second item. this will give you a strong powerspike, allowing you to act as a pseudo assassin with your roams rather than a utility ganker. Now in the full build section of the items, the last 4 items are interchangable based on matchups. Ideally you go muramana into ravenous hydra, allowing you to hyperfarm with the aoe passive, but this will only work best in stalemate midgames. Now more detail on powerspikes.
AD Asol has a very distinct power curve. you have a small spike at level 6, as your ult gives you more cc to hit more stars. Your next spike is muramana, which you can either build first or second, however building it second prevents your team from "ff 15"ing, as well as giving you more time to stack tear. however, after this, your power no longer spikes, and instead steadily increases. Finally, we reach the playstyle. Your goal is to teamfight and stall. Once you are 3-4 items deep into your build, you are a near unkillable raidboss. For the early game, follow your jungler for 2 man ganks with your e, and to secure objectives. if you get all the dragons, then the enemy cannot, this slows their powercreep, allowing you to more safely outscale.