I'd appreciate your guidance on the rules governing the picking up of a dropped item within 5e and Adventurers League rules.
Here are two scenarios:
My character, equipped with a two-handed weapon, uses the Battle Master maneuver "Disarming Attack" on a wizard causing him to drop his wand at his feet. Can I use the "Other Activity On Your Turn" mechanic to pick up the wand and stow it in my belt? Although I am carrying a two-handed weapon, since this is the "Other Activity On Your Turn" mechanic and I am not attacking with the weapon for the moment, I would like to assume that I can use one of my hands to pick up and stow the wand, and then return that hand to the pommel of the two-handed sword.
Does your answer change if I am using a one-handed weapon and have a free hand?
Here is the text in the Player's Handbook (page 74) regarding "Disarming Attack":
When you hit a creature with a weapon attack, you can expend one superiority die to attempt to disarm the target, forcing it to drop one item of your choice that it's holding. You add the superiority die to the attack's damage roll, and the target must make a Strength saving throw. On a failed save, it drops the object you choose. The object lands at its feet.
Here is the text in the Player's Handbook (page 190) regarding "Other Activity On Your Turn": (Personal note: the term "free action" does not seem to appear in 5E)
Your turn can include a variety of flourishes that require neither your action nor your move... You can also interact with one object or feature or the environment for free, during either your move or your action. For example, you could open a door during your move as you stride toward a foe, or you could draw your weapon as part of the same action you use to attack. The DM might require to use an action for any special care or when it presents an unusual obstacle. For instance, the DM could reasonably expect you to use an action to open a stuck door or turn a crank to lower a drawbridge.
So I'd appreciate your guidance on the rules and mechanics governing this situation.