Question: What suburban county on Long Island and the easternmost county in the U.S. state of New York is the location of a village called Lindenhurst?

full_context: Document 1: Riverhead (town), New York: Riverhead is a town within Suffolk County, New York, on the north shore of Long Island. As of the 2010 census, the population was 33,506. The town rests on the mouth of the Peconic River, from which it derives its name. Since 1727, Riverhead has been the county seat of Suffolk County. The smaller hamlet of Riverhead lies within it, and is the town's principal economic center. The town is 166 miles (267 km) southwest of Boston via the Orient Point-New London Ferry, and is 76 miles (123 km) northeast of New York City.
Document 2: Patchogue, New York: Patchogue is a village on the south shore of Long Island in Suffolk County, New York, United States. The population was 11,798 at the time of the 2010 census. Patchogue is part of the town of Brookhaven, on the South Shore of Long Island, adjoining Great South Bay. It is officially known as the Incorporated Village of Patchogue.
Document 3: Levittown, New York: Levittown, formerly Island Trees, is a hamlet and census-designated place (CDP) in the Town of Hempstead in Nassau County, New York on Long Island. It is located half way between the villages of Hempstead and Farmingdale. As of the 2010 census, the CDP had a total population of 51,881, making it the most populated CDP in Nassau County and the second most populated CDP on Long Island, behind only Brentwood.
Document 4: 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.
Document 5: Village of the Branch, New York: Village of the Branch is a village in the Town of Smithtown in Suffolk County, New York, United States. The population was 1,807 at the 2010 census. The village incorporated in 1927.
Document 6: Freeport, New York: Freeport (officially The Incorporated Village of Freeport) is a village in the town of Hempstead, Nassau County, New York, USA, on the South Shore of Long Island. The population was 43,713 at the 2010 census. A settlement since the 1640s, it was once an oystering community and later a resort popular with the New York City theater community. It is now primarily a bedroom suburb but retains a modest commercial waterfront and some light industry.
Document 7: Suffolk County, New York: Suffolk County is a suburban county on Long Island and the easternmost county in the U.S. state of New York. As of the 2010 census, the county's population was 1,493,350, estimated to have decreased to 1,492,583 in 2016, making it the fourth-most populous county in New York. Its county seat is Riverhead, though most county offices are located in Hauppauge. The county was named after the county of Suffolk in England, from where its earliest European settlers came.
Document 8: Suffolk County Transit: Suffolk County Transit is the provider of bus services in Suffolk County, New York on Long Island in the United States and is an agency of the Suffolk County government. It was founded in 1980 as a county-run oversight and funding agency for a group of private contract operators which had previously provided such services on their own. While the physical maintenance and operation of the buses continue to be provided by these providers, other matters ranging from bus purchases to route and schedule planning to fare rules are set by Suffolk Transit itself.
Document 9: Babylon, New York: Babylon is one of ten towns in Suffolk County, New York, United States. Located on Long Island, the town population was 214,191 as of the 2014 census. Parts of Jones Beach Island, Captree Island and Fire Island are in the southernmost part of the town. It borders Nassau County to the West, and the Atlantic Ocean to the South. At its westernmost point, its location is approximately 20 mi from New York City at the Queens border, and approximately 30 mi from Manhattan. There is also a village of Babylon located within the town.
Document 10: Nassau County, New York: Nassau County is a suburban county on the western side of Long Island in the U.S. state of New York. At the 2010 census, the county's population was 1,339,532, estimated to have increased to 1,361,500 in 2016. The county seat is in the Village of Garden City, within the boundaries of the Mineola 11501 zip code.
Document 11: Fire Island: Fire Island is the large center island of the outer barrier islands parallel to the south shore of Long Island, New York. In 2012, Hurricane Sandy once again divided Fire Island into two islands. Together, these two islands are approximately 31 mi long and vary between 160 and wide. Fire Island is part of Suffolk County. It lies within the towns of Babylon, Islip, and Brookhaven, containing two villages and a number of hamlets. All parts of the island not within village limits are part of the Fire Island census-designated place (CDP), which had a permanent population of 292 at the 2010 census, though that expands to thousands of residents and tourists during the summer months.
Document 12: Lindenhurst, New York: Lindenhurst is a village in Suffolk County, New York, United States, on the southern shore of Long Island in the town of Babylon. The population was 27,253 at the 2010 census.
Document 13: Islip, New York: Islip ( ) is one of ten towns in Suffolk County, New York (USA). Located on the South Shore of Long Island, the town population was 335,543 at the 2010 census. Within the Town of Islip is a smaller, unincorporated hamlet and census-designated place also named Islip.
Document 14: Lindenhurst Senior High School: Lindenhurst Senior High School (LSHS) is a public high school in Lindenhurst, New York on the South Shore of Long Island. The high school is the sole high school of the Lindenhurst Union Free School District, which includes the Village of Lindenhurst and North Lindenhurst.
Document 15: Bay Shore, New York: Bay Shore is a hamlet and census-designated place (CDP) in the Town of Islip, Suffolk County, New York, United States. It is situated on the South Shore of Long Island, adjoining the Great South Bay. In 2008, Bay Shore celebrated the 300th anniversary of the purchase of the land from the Secatogue Native Americans. The population of the CDP was 26,337 at the time of the 2010 census.
ground_truth: Suffolk County