There's a few approaches, probably case-dependent, but in the jury room arguing for "reasonable doubt" and not letting anyone convince you otherwise is likely the move - "cop could be lying", "state didn't show any real evidence" (like no forensics), use the defense's arguments, etc. etc.
just say something like "While I agree that this person committed the crime, I feel like the punishment for doing so is excessive and I couldn't in good faith impose that on them"
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In this guy's place, I'd do the same thing and so would you
"Not guilty" is the default. "Guilty" is what you vote if you think the prosecutors proved their case.