[RPG] way to leave melee combat without provoking an opportunity attack

No.

You have to choose to Power Attack on your turn as part of your attack action:

On your action, before making attack rolls for a round...

And the AoO rules say...

Attack of Opportunity

You threaten all squares into which you can make a melee attack, even when it is not your action.

Attacks of opportunity are special attacks -- they are not a type of action.

When it is your action (your turn), you can choose to make a Power Attack, before you make your attack rolls. You then get the Power Attack bonus for all melee attacks until the beginning of your next turn. This means you do (and must) apply your Power Attack bonus to an attack of opportunity, but only for an AoO made after the action in which you made a Power Attack and before your next turn.

Since it may not be obvious based on the comments I'm getting, the "on your action" language is almost definitely an accidental hold-over from the 3e rules, as mentioned in KRyan's answer. It is not intended to mean on any action, but specifically on your turn.

There are no facing rules in 5e by default. Thus one provokes an OA leaving an opponent's reach no matter how you imagine the characters are faced. The reasoning behind this is that the round represents six seconds of movement: thrusts, parrying, bobbing-and-weaving, &c.^*

In your example, the answer is: yes, Atone would provoke an OA from Dip.

If you really want facing turn to the DMG. P.252 describes "Optional Rule: Facing." However, this optional rule says nothing about OAs. In my opinion it wouldn't be much of a stretch to discuss a reasonable modification to include OAs if your table chooses to use these optional rules.