Question: What is the seat of the county that includes the villae of East Nassau, New York?

Context paragraphs:
Merrick Road: Merrick Road, known as Merrick Boulevard inside New York City, is an east–west urban arterial in Queens, Nassau, and Suffolk counties, New York, United States.  It runs east from the Queens neighborhood of Jamaica through Merrick past the county line between Nassau and Suffolk into Amityville, where it becomes Montauk Highway at the Amityville–Copiague village/hamlet line.  The easternmost portion of Merrick Road, from Carman Mill Road to its eastern terminus, signed as part of New York State Route 27A (NY 27A).  At one time, the entire length of Merrick Road was signed as NY 27A; currently, the entire portion within Nassau County is currently designated as the unsigned County Route 27 (CR 27).  Merrick Road travels along an old right-of-way that was one of the original paths across southern Long Island, stretching from Queens to Montauk Point.

Rockland County, New York: Rockland County is the southernmost county on the west side of the Hudson River in the U.S. state of New York, part of the New York–Newark–Jersey City, NY–NJ–PA Metropolitan Statistical Area.  The county's population, as of the 2010 census, was 311,687, increasing by 4.8% to a 2016 Census estimate of 326,780, making it the third most densely populated county outside of New York City within New York State (after Nassau and neighboring Westchester counties, respectively).  The county seat is New City.  Although Rockland County does not directly border any New York City boroughs, it lies only 9 miles northwest of the city at their closest points, and is accessible via the New York State Thruway, after 10 exits.  The name derives from "rocky land", as the area was described by early Dutch and English settlers.

Timeline of town creation in Downstate New York: The towns and cities of Downstate New York were created by the U.S. state of New York as municipalities in order to give residents more direct say over local government.  Present-day Westchester, Bronx, New York, Richmond, Kings, Queens, Nassau, and Suffolk counties were part of York Shire from 1664-August 1673 and again from February 1674 until 1683 at which point the Province of New York was divided into counties.  From August 1673 to February 1674 New York was under Dutch control and English political units were suspended, then restored under English rule.  York Shire was divided into three divisions called ridings, the East, West, and North ridings.  In 1683 the colony of New York eliminated shires and ridings in favor of counties, the East Riding becoming Suffolk County, West Riding the counties of Richmond and Kings, while the North Riding became the counties of Westchester (including present-day Bronx), New York, and Queens (including present-day Nassau).

Rensselaer County, New York: Rensselaer County is a county in the state of New York, in the United States of America.  As of the 2010 census, the population was 159,429.  Its county seat is Troy.  The county is named in honor of the family of Kiliaen van Rensselaer, the original Dutch owner of the land in the area.

Old Nassau County Courthouse (New York): The Old Nassau County Courthouse, also known as the Nassau County Courthouse and the Historic Nassau County Courthouse, is an historic 2-story courthouse building located at 1550 Franklin Avenue in Garden City, Nassau County, New York.  Designed by noted New York City architect William B. Tubby in the Classical Revival style of architecture with a grand rotunda capped by a white dome, it was built of poured-in-place reinforced concrete.  Then governor Theodore Roosevelt laid its cornerstone in 1900 and it was finished in 1901.  Wings designed by Tubby were added in 1916.  Later additions and renovations were 1924-1928 under the supervision of architect William J. Beardsley, who had designed the Dutchess County Court House in Poughkeepsie.

East Nassau, New York: East Nassau is a village in Rensselaer County, New York, United States.  The population was 587 at the 2010 census.

Green Acres Mall: Green Acres Mall is an indoor shopping mall located in South Valley Stream, New York, off Sunrise Highway in Nassau County right off the border of New York City and the Incorporated Village of Valley Stream (part of the parking lot and stores on the north side of the property are in the Village, while the mall itself is in an unincorporated hamlet of the Town of Hempstead).  The mall has a gross leasable area (GLA) of 1800000 sqft .  The mall is the 26th largest in the United States.  The mall is extremely popular in Nassau County and in the neighboring New York City borough of Queens.  The mall is accessible by many Nassau Inter-County Express routes as well as two MTA New York City Bus routes, the Q5, Q85, that cross the city border.

East Nassau Central School: East Nassau Central School is a historic school building located at East Nassau in Rensselaer County, New York.  It was built in 1930 and is a two story, steel frame and concrete block building with a brick veneer in the Classical Revival style.  It sits upon a raised concrete foundation and has a flat roof concealed behind a low parapet wall with concrete capstones.  It features a small entrance portico of brick with concrete trim and a wrought iron balustrade.

Long Island: The Long Island is a large, densely-populated island off the East Coast of the United States, beginning at New York Harbor just 0.35 miles (0.56 km) from Manhattan Island and extending eastward into the Atlantic Ocean.  The island comprises four counties in the U.S. state of New York: Kings and Queens (which comprise the New York City boroughs of Brooklyn and Queens, respectively) to the west; and Nassau and Suffolk to the east.  However, many people in the New York metropolitan area (even those living in Brooklyn and Queens) colloquially use the term "Long Island" (or "The Island") exclusively to refer to the Nassau–Suffolk county area collectively, which is mainly suburban in character.  The majority of New York City residents now live on Long Island.

Brainard, New York: Brainard is a hamlet in the town of East Nassau, Rensselaer County, New York, United States.  The community is located along U.S. Route 20 and New York State Route 66 5.2 mi east-south east of the village of Nassau.  Brainard has a post office with ZIP code 12024, which opened on April 7, 1881.

Supporting paragraphs: East Nassau, New York Rensselaer County, New York
Answer: Troy