but my own experience has been that once the fire is detected, sit on your hands and count to ten, then address the problem with a workable cadence and some measured patience.
The 10 seconds that you sit on your hands could cost you your life. You have no idea of the severity of the fire - it could even be a false fire warning. But you simply do not know. The advice in the Boeing 737 FCTM is all you can go by and that says:
"Indications of an engine fire, impending break-up or approaching engine limits, should be dealt with as soon as possible."
Don't purposely build in breathing space just because you fear you may stuff things up. There is no shortage of advice from well meaning simulator instructors or other pilots when it comes to defining engine fire action drills.