Word to refer to two opposite words [duplicate]

For the sentence

Depending on your behavior, you will be (single word for rewarded or punished) appropriately.

I'd suggest the word treat, thusly

Depending on your behavior, you will be treated appropriately.

Chambers defines treat as to deal with; to handle (and a fair bit besides, but those are the germane meanings here). In isolation a treat is more likely to be a reward than a punishment, it fits the sentence in the question, but may fall short of being a general replacement in similar sentences.

As to the second part of the question, I don't have any useful suggestions for a single word. But my search strategy would include finding synonyms for both terms and looking for common words. From the dictionary on my desk I found desert(s) as a synonym for both reward and punishment. Admittedly, this suggests my search strategy is not a terrifically good one, but it did find a word synonymous with both others!