Question: Which ruined castle in South Lanarkshire, Scotland overlooks the River Nethan?

Context articles: Auchenheath
List of places in South Lanarkshire
Hamilton, South Lanarkshire
Craignethan Castle
NHS Lanarkshire
Nethan Gorge
Boghead
River Nethan
Lanarkshire Area Tourism Partnership
Rosebank, South Lanarkshire

Auchenheath is a small village in South Lanarkshire, Scotland.
 It is on the River Nethan and is located near Blackwood, Kirkmuirhill, and Lanark.
The List of places in South Lanarkshire is a list of links for any town, village, hamlet, castle, golf course, historic house, hillfort, lighthouse, nature reserve, river, and other place of interest in the South Lanarkshire council area of Scotland.
Hamilton is a town in South Lanarkshire, in the central Lowlands of Scotland.
 It serves as the main administrative centre of the South Lanarkshire council area.
 It is the fourth-biggest town in Scotland.
 It sits 12 mi south-east of Glasgow, 35 mi south-west of Edinburgh and 74 mi north of Carlisle, Cumbria.
 It is situated on the south bank of the River Clyde at its confluence with the Avon Water.
 Hamilton is the later county town of Lanarkshire which was preceded anciently by Lanark.
Craignethan Castle is a ruined castle in South Lanarkshire, Scotland.
 It is located above the River Nethan, a tributary of the River Clyde, at [ NS816464] .
 The castle is two miles west of the village of Crossford, and 4.5 miles north-west of Lanark.
 Built in the first half of the 16th century, Craignethan is recognised as an excellent early example of a sophisticated artillery fortification, although its defences were never fully tested.
NHS Lanarkshire is responsible for the health care of more than 652,230 people living within the council areas of North Lanarkshire and South Lanarkshire in Scotland, making it the third largest health board in the country after NHS Greater Glasgow & Clyde and NHS Lothian.
 NHS Lanarkshire employs approximately 12,000 staff.
 The board is based at Kirklands, Fallside Road in Bothwell, South Lanarkshire.
Nethan Gorge is a natural gorge carved by the River Nethan, located in South Lanarkshire, Scotland.
Boghead is a small village in South Lanarkshire, west central Scotland.
 It is about 23 mi southeast of Glasgow and sits nearby to the River Nethan and Avon Water.
 Boghead is a residential area, with working residents commuting to nearby villages and large towns of Lesmahagow, Strathaven and Lanark.
 It is composed of houses built along Strathaven Road (the B7086) and Lesmahagow Road.
 It originated in the early 19th century around the old Blackwood Estate, as the original inhabitants used to work there.
The River Nethan is a river which flows between Glenbuck in East Ayrshire and Crossford, South Lanarkshire where it feeds into the River Clyde, with the town of Lesmahagow and surrounding villages sitting on the river course.
 The area of woodland surrounding the River Nethan at Crossford and Auchenheath has been declared a site of special scientific interest and forms a part of the Clyde Valley Woodlands National Nature Reserve as Nethan Gorge.
 Craignethan Castle, a 16th-century fortification, overlooks the river.
The Lanarkshire Area Tourism Partnership (formerly Lanarkshire Strategic Tourism Marketing Partnership) created the strategy for tourism and economic development in Lanarkshire under the brand "VisitLanarkshire" in 2005.
 This partnership is made up of representatives from North Lanarkshire and South Lanarkshire councils, VisitScotland, and private organisations across Lanarkshire, and is funded by the Lanarkshire Tourism Association.
 The development of tourism is in line with the objectives set out in the Lanarkshire Tourism Action Plan.
Rosebank is a small hamlet situated in South Lanarkshire, Scotland.
 With a population of around 200, Rosebank is one of the least-populated settlements in South Lanarkshire.
 The hamlet is situated on the banks of the River Clyde, and was constructed by Lord Newlands of Mauldslie Castle (which stood in the Mauldslie Woods area across the Clyde) for estate workers.