Legalizing recreational marijuana. Earlier this year, Mr. Cuomo studied legalizing marijuana in the state. A report issued by the Health Department concluded that the state should have a regulated and taxed market for marijuana. In the past, Senate Republicans have refused to take up the issue, saying that legalizing marijuana was not a priority for them.

Strengthen rent regulation. Facing an affordable housing crisis in the city, a Democrat-run Legislature could roll back some of the changes made to the rent regulation system in the last few decades. They could end rules that take apartments out of regulation when the rent hits $2,733.75 and end the 20 percent bonus that landlords are allowed to tack on to rent when a tenant vacates.

Writing Roe v. Wade protections into state law. In the past, Mr. Cuomo has pushed legislation that would codify the protections guaranteed under Roe v Wade into state law and update the state’s law to allow late-term abortions when the health of the mother is in danger or the fetus is not viable. Senate Republicans have stymied the bill’s passage in the past, but Mr. Cuomo said he wants it passed during the first month of the new legislative season.

Single payer health care. While it might be a pipe dream for Democrats, the State Assembly has passed a measure to create a single payer health care system for the last four years in a row. The proposal would allow New Yorkers to sign on to health coverage without deductibles or copays. Republicans were unwilling to take up the measure when it was last passed by the Assembly in June.