In my eyes there's 2 optimal ways to play the d1.
The aggressive town method
1) Cop outs, leads a lynch and forces a lynch when they feel like it. We hesitate to sheep it and if the chosen person is doc (or mafia perhaps) they claim doctor and we don't lynch. If not, we lynch and on n2 the doc saves cop etc. This makes us more aggressively capable on d2 even if the doc dies as long as the cop's investigation wasn't the doc.
The less blood-thirsty town method
No one outs, no one talks. Instant no-lynch. We let Maf give it a go.
Which one we pick is important but it would be helpful if cop did NOT OUT until consent has been given to the aggressive method.
Note for the aggressive
If cops is coutner-claimed (cc'd) we nolynch as well (it's very optimal).