Purchased $85 of advertising in this month's local paper on credit; cash payment due in a month.

Assets are debit entries, but so are expenses. What do you think you should debit?

I would like to clear up the false assumption that's in your subject title: What asset account do I increase if I increase accounts payable?

That question doesn't work. New students get the idea that certain accounts always go together and that you're doing one thing because of what the other account is. In other words, increasing an accounts payable simply means you now owe more than you used to - but there is nothing in that which dictates what other account should be used. You could owe more money for any number of reasons.

There's nothing about increasing accounts payable that says there's an asset at all. The two just aren't related.

You've mentioned advertising in the post itself, but the title you wrote is telling me you're making the assumption about things being used just because accounts payable is being used, and that just doesn't exist.

There's always at least two accounts for every entry. In your entry, the accounts payable has nothing to do with what other account is being used. You can just as easily have paid cash and the other account will remain the same. You have to learn to separate the statements in the transaction and find the parts that tell you what each account is.

"Purchased $85 of advertising in this month's local paper" - this is what tells you what the other account is - the payable isn't related to it.

You will have an expense account and a liability account