How low is low? My engine stoppage happened at about 2000 AGL. (Likely induction or carb icing) Pitch to best glide, pick out a landing spot, then go through the engine stoppage troubleshooting memory list (carb heat, mags, fuel pump, switch fuel tank, mixture). Engine restarted at 500 AGL, otherwise landing in a flat snowy field. My copilot/IPC instructor was hovering over the fuel selector if we were committed to an off-airport landing. Much lower and I would not have had much time for the troubleshooting list. Fly first, troubleshoot as time permits.
I've also had a partial power anomaly (excessive engine vibration) just after takeoff (100 AGL) after a cylinder replacement. That one scared the bejeebers out of me. My initial thought was a cylinder valve failure. Reduced power slightly to reduce vibration and buy some time if the engine was going, picked on a landing spot (golf course fairway off the runway end). Fortunately I could maintain adequate airspeed in a shallow climbing turn to gain more altitude and options while remaining within gliding distance of the crossing runway and/or golf course. Reached pattern altitude and did some very quick troubleshooting (mags, already at full rich and fuel pump on for takeoff, didn't seem to be a fuel issue, mag switching no help), pulled power and landed immediately on the runway. Turned out to be a failed spinner.
The common thread: maintain adequate airspeed, pick out the safest emergency landing spot, troubleshoot later (if time).
Unfortunately, at our airport we had a newly minted pilot (100 hours experience) rent a C172, somehow encounter carb icing on a CAVU fall day, and manage to stall and spin the plane into a large farm field that was an ideal off-airport landing spot. To avoid this kind of fate, you need to brush up on your emergency procedures and put it into action when an anomaly strikes. My primary instructor many years ago drilled that into each and every student. I'm glad he did. Not only did we do the ritual "your engine failed" on almost every flight, we also did aborted takeoffs as well. (And I've had to implement an aborted takeoff, too, in real life flying.) Stay safe out there.