...assess the situation, look for your place to land and if you can find a way back to the airport great.
Yes. Every situation is different. Wind, density altitude, weight, souls on board, configuration, terrain, etc.
Every plan to know your numbers to pick the altitude to commit to the impossible turn is at best an estimate, and doesn't factor in the "fluster" factor. I doubt anybody can shorten the 4 to 6 seconds (or more) to get the nose down and fully comprehend what WTH is happening, before putting the "save my butt plan" in place.... if there even is one. You can't hold altitude, and you're descending at a rate that is giving you visual cues, not instrument indications and calculations. Your brain better be 100% focused on survival. And that means ignoring that common practice of announcing the engine has fails and I'm coming back. ATC or pilots on the receiving end of a panicked radio are the least of your problems (or help).
My plan for engine loss on takeoff has evolved over the years into pure simplicity. Excuse the goofiness. I call it the Pizza Principle.
The aircraft is sitting in the center of a Pizza Pie, not yet cooked. The outer edge of the slices represent an arc and within the region and boundaries of what you positively know you can reach (with an extra 5 -10 knots carried for rough maneuvering if necessary) to make the threshold of the touchdown point in the most survivable spot you pick within region represented by the slice of pizza under then around the plane.
After lift off, if it quits real low, head straight ahead on the runway remaining, or whatever is off the end plus or minus a swerve or minor change of direction between hard objects to fly plane as deep into the crash as possible.
As a normal climb continues, the aircraft climbs and the pizza pie starts growing with altitude. The higher you climb, the more slices are cooked. You have to be continually glancing outside and determining which general direction to point the plane at if it quits "right now" over the cooked area of the pie, which represents what you know you can reach.
At some point you have a half a pie when the slices reach the wingtips. Don't even bother looking to the rear of the wings that you don't think you can make if it quits right then. This gives your brain more focus on surviving what's reachable.
At some point the pie becomes complete, and only then should you consider the impossible turn, which is now possible.
You need to know your plane and the difference between a good glide, and a brick, under different configurations. It's a visual process, and not numberic.