What's my strategy for buying this car?

So I have a vehicle picked out that I’m interested in that has been sitting on the dealer’s lot since mid December. It’s a Toyota but not one that has been involved in the recall.
Sticker price: $29,835
Edmund’s quoted invoice price: $27,119
Edmund’s “what others are paying” price: $27,894
there is a $750 manuf. rebate available on it
Edmund’s “what others are paying” price with rebate: $27,144
They have it on the lot with a “sale” sign in the window for $27,550

So what price do I aim for and where do I start? Their rebate adjusted invoice price would bring it down to $26,369.

Do I go in and ask them straight up “what is the absolute lowest price you’ll sell that to me for today?”
Do I set a price and tell them straight up “I’ll take that vehicle off your hands right now for X$”? With an artificially low price? With an actual target price?

How much over this adjusted invoice price should I really pay? $200? $500? The Edmunds suggested $775?

here’s my philosophy for haggling with car dealers- They’d much rather make a quick sale today then wring the last penny out of you if it takes more time. Tell them you’re going to put down money now if they give you a great price. Then they’ll ask you what a “great” price means. Tell them $26,400. Pull out the checkbook & ask how to make out the downpayment check. Just be clear that the sale will close in the next 5 minutes if you get your price.

Audient said. And be prepared to walk away. Give them your number in case they change their mind. Even leave the lot. They will call you. Especially if the car has been sitting their for 2 months,