Question: What river's banks was the castle on where Andrew Dudley participated in the War of the Rough Wooing?

full_context: Document 1: Loch Leven Castle: Loch Leven Castle is a ruined castle on an island in Loch Leven, in the Perth and Kinross local authority area of Scotland. Possibly built around 1300, the castle was the location of military action during the Wars of Scottish Independence (1296–1357). In the latter part of the 14th century, the castle was granted by his uncle to William Douglas, 1st Earl of Douglas, and remained in Douglas' hands for the next 300 years. Mary, Queen of Scots was imprisoned here in 1567–1568, and forced to abdicate as queen, before escaping with the help of her gaoler's family. In 1588, the Queen's gaoler inherited the title Earl of Morton, and moved away from the castle. It was bought, in 1675, by Sir William Bruce, who used the castle as a focal point in his garden; it was never again used as a residence.
Document 2: Findlater Castle: Findlater Castle is the old seat of the Earls of Findlater and Seafield, sitting on a 50 ft -high cliff overlooking the Moray Firth on the coast of Banff and Buchan, Aberdeenshire, Scotland. It lies about 15 km west of Banff, near the village of Sandend, between Cullen and Portsoy. The cliffs here contain quartz; the name "Findlater" is derived not from Norse as earlier stated here, but from the Scots Gaelic words "fionn" ("white") and "leitir" ("cliff or steep slope"). The first historical reference to the castle is from 1246. King Alexander III of Scotland repaired this castle in the 1260s in preparation for an invasion by King Haakon IV of Norway. The Vikings took and held the castle for some time. The castle remains that are still there are from the 14th-century rebuilding, when the castle was redesigned based on the Roslyn Castle model.
Document 3: Rough Wooing: The Rough Wooing (December 1543 – March 1551) was a war between Scotland and England. Following its break with Rome, England decided to attack Scotland, partly to destroy the Auld Alliance, and prevent Scotland being used as a springboard for future invasion by France, partly to weaken Scotland, and partly to force Scotland to agree to a marriage alliance between its child Queen Mary and the English heir apparent Edward, son of King Henry VIII. An invasion of France was also contemplated. War was declared by Henry in an attempt to force the Scots to agree to a marriage between Edward and the infant queen, thereby creating a new alliance between Scotland and England. Edward, crowned king in 1547 at the age of nine, continued the war for a time under the direction of the Duke of Somerset before Somerset's removal from power in 1549 and replacement by the Duke of Northumberland, who wished for a less costly foreign policy than his predecessor. It was the last major conflict between Scotland and England before the Union of the Crowns in 1603, excepting perhaps the English intervention at the Siege of Leith in 1560, and was part of the Anglo-Scottish Wars of the 16th century.
Document 4: Ardrossan Castle: Ardrossan Castle is situated on the west coast of Scotland in the town of Ardrossan, Ayrshire. The castle, defended by a moat, stands on a ridge above the town. There is a keep dating from the fifteenth century, and a vaulted range containing a kitchen and cellars. In a deep passageway there is a well. Part of the keep remains up to the corbels of the parapet, but it is in ruins. The original castle, owned by Clan Barclay, was partly destroyed during the Wars of Scottish Independence. This event, in which the English garrison were slaughtered, became known as "Wallace's Larder," a name which is still applied to the remaining vaults. Rebuilt by Clan Montgomery in the 15th century, Ardrossan later fell into disuse and was partially demolished by the soldiers of Oliver Cromwell in the 17th century who used the stones to help construct the Ayr Citadel.
Document 5: Dunderave Castle: Dunderave Castle is an L-plan castle built in the 16th century as the Scottish seat of the MacNaughton clan. The castle lies on a small promontory on the northern shores of Loch Fyne, around 5 km north-east of Inveraray, Argyll. The castle is in use as a residence. The present castle was built after their previous castle was destroyed following a Plague infection. The old castle, and remnants of McNaughton crannógs, can still be seen on the lochan known as the Dubh Loch at the head of Glen Shira.
Document 6: Douglas Castle: Douglas Castle was a stronghold of the Douglas family from medieval times to the 20th century. The first castle, erected in the 13th century, was destroyed and replaced several times until the 18th century when a large mansion house was built in its place. This too was demolished in 1938, and today only a single corner tower of the 17th-century castle remains. The castle was the former family seat of the Prime Minister, Sir Alec Douglas-Home. The castle was located around 1 km north-east of the village of Douglas, South Lanarkshire, in south-west Scotland. The remains are protected as a category C listed building.
Document 7: Lord Henry Seymour (naval commander): Lord Henry Seymour was a younger son of Edward Seymour, 1st Duke of Somerset by his second wife Anne Stanhope. Aboard HMS "Rainbow" he commanded the 'Narrow Seas' Squadron of ships that took part in the Battle of Gravelines against the Spanish Armada in 1588. Controlling the seas off Dunkirk they joined the main British fleet (the 'Western Squadron') near Calais on 6 August, adding about a third to the total size.
Document 8: Andrew Dudley: Sir Andrew Dudley, KG (c. 1507 – 1559) was an English soldier, courtier, and diplomat. A younger brother of John Dudley, 1st Duke of Northumberland, he served in Henry VIII's navy and obtained court offices under Edward VI. In 1547–1548 he acted as admiral of the fleet and participated in the War of the Rough Wooing in Scotland, where he commanded the English garrison of Broughty Castle. He was appointed captain of the fortress of Guînes in the Pale of Calais in late 1551. There he got involved in a dispute with the Lord Deputy of Calais, which ended only when both men were replaced in October 1552.
Document 9: Broughty Castle: Broughty Castle is a historic castle on the banks of the river Tay in Broughty Ferry, Dundee, Scotland. It was completed around 1495, although the site was earlier fortified in 1454 when George Douglas, 4th Earl of Angus received permission to build on the site. His son Archibald Douglas, 5th Earl of Angus was coerced into ceding the castle to the crown. The main tower house forming the centre of the castle with four floors was built by Andrew, 2nd Lord Gray who was granted the castle in 1490.
Document 10: Fetteresso Castle: Fetteresso Castle is a 14th-century towerhouse, rebuilt in 1761 as a Scottish gothic style Palladian manor, with clear evidence of prehistoric use of the site. It is situated immediately west of the town of Stonehaven in Kincardineshire slightly to the west of the A90 dual carriageway. Other notable historic fortified houses or castles in this region are Dunnottar Castle, Muchalls Castle, Fiddes Castle, Cowie Castle and Monboddo House.
Document 11: Andrew Murray (Scottish soldier): Sir Andrew Murray (1298–1338), also known as Sir Andrew Moray, or Sir Andrew de Moray, was a Scottish military and political leader who supported David II of Scotland against Edward Balliol and King Edward III of England during the so-called Second War of Scottish Independence. He held the lordships of Avoch and Petty in north Scotland, and Bothwell in west-central Scotland. In 1326 he married Christina Bruce, a sister of King Robert I of Scotland. Murray was twice chosen as Guardian of Scotland, first in 1332, and again from 1335 on his return to Scotland after his release from captivity in England. He held the guardianship until his death in 1338.
Document 12: Richard Weston (treasurer): Sir Richard Weston (1465–1541), KB, of Sutton Place in Surrey, was a courtier and diplomat who served as Governor of Guernsey, Treasurer of Calais and Under-Treasurer of the Exchequer during the reign of King Henry VIII.
Document 13: Barnbougle Castle: Barnbougle Castle is a much-altered tower house on the southern shore of the Firth of Forth, between Cramond and Queensferry, and within the parish of Dalmeny. It lies within the Earl of Rosebery's estate, just northwest of Dalmeny House. Although its history goes back to the 13th century, the present castle is the result of rebuilding in 1881 by the 5th Earl of Rosebery, who served as Prime Minister from 1894–1895.
Document 14: Siege of Haddington: The Sieges of Haddington were a series of sieges staged at the Royal Burgh of Haddington, East Lothian, Scotland, as part of the War of the Rough Wooing one of the last Anglo-Scottish Wars. Following Regent Arran's defeat at the battle of Pinkie Cleugh on Saturday 10 September 1547, he took Haddington, with 5000 troops including French mercenaries and troops sent by Henry II of France to bolster the Auld Alliance. Afterwards, Francis Talbot, 5th Earl of Shrewsbury took it with nearly 15000. The English forces built artillery fortifications and were able to withstand an assault by the besieging French and Scots troops supported by heavy cannon in July 1548. Although the siege was scaled down after this unsuccessful attempt, the English garrison abandoned the town on 19 September 1549, after attrition by Scottish raids at night, sickness, and changing political circumstance.
Document 15: Siege of Sluis (1587): The Siege of Sluis of 1587 took place between 12 June and 4 August 1587, as part of the Eighty Years' War and the Anglo-Spanish War (1585–1604). On 12 June 1587, Don Alexander Farnese, Duke of Parma "(Spanish: Alejandro Farnesio)", Governor-General of the Spanish Netherlands, and commander-in-chief of the Army of Flanders, laid siege to the strategic deep-water port of Sluis, defended by English and Dutch troops under Sir Robert Dudley, Earl of Leicester, Governor-General of the United Provinces, and Sir Roger Williams. On 24 June, the bombardment began, and on 4 August, after of 13 days of constant fighting around the walls, the English garrison surrendered.<ref name="Parker/Martin p. 126–127">Parker/Martin p. 126–127</ref> The loss of the English-held port of Sluis revealed the inability of Leicester to assert his authority over the Dutch allies, who refused to cooperate in relieving the town, and led to recriminations between the governor-general and the States of Holland.
ground_truth: Tay