One vital thing to do in the event of an engine failure is to "push"
There are rather a lot of people who would disagree violently with that.
First action in the event of an engine failure in a single-engine type is to achieve, maintain, and trim for best glide speed, whilst searching for a suitable landing area. Once that has been identified
- plan your circuit
- try to identify the reason for the failure
- decide whether a restart is desirable or likely to be successful
- get out a mayday call
- carry out shut-down and security checks.