Question: Palm Springs lies in Palm Beach County, the third most populated county in its state. Which major U.S. city is it near?

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Palm Tran is the public transit bus system run by the Palm Beach County Government, serving Palm Beach County, Florida.  During fiscal year 2015, Palm Tran provided 10,773,132 one-way passenger trips and 889,056 paratransit trips to Palm Beach County.  Palm Tran also serves a portion of Broward County, Florida where it overlaps with Broward County Transit.  Palm Tran has four main facilities (North Campus in West Palm Beach, South Campus in Delray Beach, Palm Tran Connection/Military Trail and the Belle Glade Facility) with its main headquarters in West Palm Beach on Electronics Way.  The current Executive Director is Clinton B. Forbes. North Palm Beach County Airport (FAA LID: F45) , also known as North County Airport, is an uncontrolled general aviation airport located 12 nautical miles (22 km) northwest of West Palm Beach off the Bee Line Highway in Palm Beach Gardens, Florida.  The airport is owned by Palm Beach County and operated by the Palm Beach County Airports Department. Cloud Lake is a town in Palm Beach County, Florida, United States.  With a population of 135 during the 2010 census, Cloud Lake is the least populous municipality in Palm Beach County.  The town is situated adjacent to Glen Ridge and West Palm Beach and is located near the Palm Beach International Airport.  Established in 1951, Cloud Lake was built largely by the efforts of twin brothers Karl and Kenyon Riddle, the former of whom served as the City Manager and Superintendent of Public Works of West Palm Beach in the 1920s. West Palm Beach is a city in and the county seat of Palm Beach County, Florida, United States.  It is one of the three main cities in South Florida.  The population was 100,343 (revised) at the 2010 census.  The University of Florida Bureau of Economic and Business Research (BEBR) estimates a 2016 population of 108,896, a 7.9% increase from 2010.  It is the oldest municipality in the Miami metropolitan area, having been incorporated as a city two years before Miami in November 1894.  Although West Palm Beach is located approximately 68 mi north of Downtown Miami, it is still considered a principal city within the Miami metropolitan area, due to the solid urbanization between both cities.  The estimated population of the Miami metropolitan area, which includes all of Palm Beach County, was 6,012,331 people at the 2015 census. Locally known as Forest Hill Boulevard, State Road 882 (SR 882) is a 9.233 mi east–west highway in Palm Beach County, Florida.  It extends from an intersection of US 441-SR 7 in Wellington, heading east serving Greenacres, Palm Springs, Lake Clarke Shores, and West Palm Beach before its eastern terminus is an intersection with South Dixie Highway (US 1/SR 805) in West Palm Beach.  It is a primary commuter road for the region. There are four "Century Villages" in south Florida, built by the same developer: West Palm Beach (Palm Beach County), Boca Raton (Palm Beach County), Deerfield Beach (Broward County), and Pembroke Pines (Broward County).  This article deals only with the West Palm Beach Century Village, the only one designed a census-designated place (CDP).  All of them are gated retirement communities, whose residents must be 55 or over. Palm Springs is a village in Palm Beach County, Florida, United States, situated between Greenacres, Lake Clarke Shores, Lake Worth, and West Palm Beach.  As of the 2010 United States Census, had a population of 18,928.  It is a minor city of the Miami metropolitan area, which was home to an estimated 6,012,331 people at the 2015 census. Palm Beach County Glades Airport (IATA: PHK, ICAO: KPHK, FAA LID: PHK) is a county owned, public use airport in Palm Beach County, Florida, United States.  It is located three nautical miles (6 km) southwest of the central business district of Pahokee, Florida.  The airport is owned by Palm Beach County and operated by the Palm Beach County Airports Department.  It is included in the National Plan of Integrated Airport Systems for 2011–2015, which categorized it as a "general aviation" facility. Headquartered in Boynton Beach, Florida, the mission of the Literacy Coalition of Palm Beach County is to improve the quality of life of those residing in and around Palm Beach County, Florida, by promoting and achieving literacy.  The ultimate goal of the Literacy Coalition of Palm Beach County, a nonprofit organization, is to ensure that every child and every adult in Palm Beach County becomes a reader.  One in seven adults in Palm Beach County is unable to read and understand information found in books, newspapers, magazines, brochures and manuals.  Through extensive outreach and collaboration with a network of community partners, the Literacy Coalition strives to ensure that individuals who need to improve their literacy skills receive the help they need.  The organization's operates with the assistance of over 9,000 volunteers.  In 2013, the Literacy Coalition provided services to more than 25,000 adults, children and families. Palm Beach County is a county located in the state of Florida, directly north of Broward County.  As of the 2010 census, the population was 1,320,134, making it the third-most populous county in Florida.  The largest city and county seat is West Palm Beach.  Named after one of its oldest settlements, Palm Beach, the county was established in 1909, after being split from Dade County.  The county's modern-day boundaries were established in 1963.  Palm Beach County is one of the three counties in South Florida which make up the Miami metropolitan area, which was home to an estimated 6,012,331 people at the 2015 census.

Supporting sentences:
Palm Springs is a village in Palm Beach County, Florida, United States, situated between Greenacres, Lake Clarke Shores, Lake Worth, and West Palm Beach.  As of the 2010 census, the population was 1,320,134, making it the third-most populous county in Florida.  Palm Beach County is one of the three counties in South Florida which make up the Miami metropolitan area, which was home to an estimated 6,012,331 people at the 2015 census.