Which statements are correct for the conversion of hexane-2,5-dione into 3-methylcyclopent-2-en-1-one with dilute $\mathrm{NaOH}$?

1. AThe first step is an intramolecular aldol addition.
2. BThe dehydration proceeds by E1cB via an enolate.
3. CThe product is a conjugated enone.
4. DThe ring-forming step produces a six-membered ring.