Gov. Andrew M. Cuomo laid out a broad and ambitious agenda in his third State of the State speech on Wednesday, putting New York on a path that simultaneously builds on his “open for business” mantra, seeks improvement in critical areas and moves to shore up support from liberals who have not always appreciated the priorities of his first two years in office.

In that, Cuomo has made a noticeable, though not profound, tack to the left. The governor who pushed for same-sex marriage two years ago is now pushing for guarantees of women’s equality, including a stronger protection for abortion rights.

The governor who last year offered no encouragement for those seeking an increase in the state’s minimum wage moved strongly behind the effort, noting higher minimum wages in states around New York and a cost of living that the current wage doesn’t meet.

Cuomo also put his shoulder behind a bid to make New York’s gun laws the nation’s toughest. Noting that he owns a firearm, himself, Cuomo said the point wasn’t to impinge on the rights of hunters, but to protect New Yorkers against the carnage caused by assault weapons with high-capacity magazines.

Much of this is important and none of it is off the map. Indeed, women’s equality is fundamental to a fair society, and after the massacre in Newtown, Conn., and the deaths of firefighters near Rochester, arguments against better control of assault weapons are tinged with fanaticism. An increase in the minimum wage may be called for – the mere existence of one presupposes periodic increases – but that is better handled at the national level.

Cuomo also pledged not to raise taxes again this year and to push for more reforms in the state workers’ compensation system. He was adamant about acknowledging the facts of climate change to better protect the state’s coastline from the ravages of destructive storms like Sandy.

To increase trust in public officials, he proposed to reduce the state’s limits on campaign donations, now the highest in the country, and to require electronic disclosure of all donations within 48 hours.

More controversially – but also acknowledging reality – he wants to build casinos upstate to bring money into Albany and to tempt New York City residents upstate and away from Connecticut and New Jersey.

There is more: a proposed competition for 10 higher- education/private-sector, high-technology incubation clusters, backed by tax-free incentives; longer school years or school days to improve education; a new upstate marketing effort; and new power for the Public Service Commission to oversee power companies, in light of poor performances after Hurricane Sandy.

But there were also omissions. He made no mention of his plan to include a more muscular historic tax credit in the budget he will present later this month. That tax credit is critical to Buffalo’s continued revival, and we presume the governor will follow through. And he offered no words on cutting back on the unfunded mandates that are especially burdensome to municipalities and school districts with the imposition of the state property tax cap.

Still, it was, in whole, a speech that aimed New York in the direction it needs to go: business-friendlier, devoted to equality, focused on safety and education. It also acknowledges the political split in the State Senate, which he may be able to use to his advantage, peeling off Republican or Democratic votes as opportunities allow. New Yorkers will know better what Cuomo wants to achieve when, in presenting his proposed budget, he puts meat on the bones of Wednesday’s speech.