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ALBANY — For the better part of the last decade, the State Capitol was a house divided: Democrats led the Assembly, Republicans ruled the Senate and most everything got stuck in between.

Then came the blue wave of the 2018 midterms, putting Democrats in control of the entire Legislature, and giving the state’s top Democrat, Gov. Andrew M. Cuomo, a chance to enjoy the power of unity. The change has been profound: In January alone, the Legislature, led by the Assembly speaker, Carl E. Heastie, and the Senate majority leader, Andrea Stewart-Cousins, passed sweeping bills on abortion, gun safety, voting rights and immigration rights.

But a strange thing has happened amid all this one-party harmony: Ms. Stewart-Cousins and Mr. Heastie have formed a fast kinship, creating a powerful allegiance that has already challenged Mr. Cuomo’s outsize influence here.

They have both declared their commitment to reasserting the authority of the Legislature, after eight years of Mr. Cuomo strong-arming Assembly and Senate leaders into compromises, and taking credit for those accomplishments.