You figure that the gap isn't too wide... and you don't trust the ledge or the rope.

You approach the gap and prepare to make the leap. The far end of the stairs is decently high up, at about shoulder height relative to where you are standing. You brace yourself and rush up to the last few steps, making a running jump through the air! As you fly towards the steps, you grab onto the edge and manage to stop your momentum. You barely manage to hang on and solidify your grip - but it's quickly becoming apparent you overestimated how sturdy the steps would be. The stone you grabbed onto is slowly collapsing downwards!

Entirely on instinct, you flail your legs outwards and put all your energy into swinging yourself back up. You just bareky manage to boost yourself up enough to grab a more solid step. You pull yourself up faster than you even thought possible - no amount of time to get your feet back on solid ground is short enough! A few moments later, you've successfully scrambled back onto the steps, your heart racing but otherwise unscathed.

After catching your breath, you can finally resume your climb up the tower stairs. At the top you find a large wooden door, cracked slightly ajar; the plumes of purple fog you noticed flowing down the stairs are emerging from within the next room. Somehow you can tell the succubus is behind that door, likely as not waiting for your arrival. Whatever you have on hand is all you can muster... it's time to finally finish the job!