Question: Which battle ended first, Battle of the Bulge or Battle of Anzio?

full_context: Document 1: Anzio (film): Anzio (US title), also known as Lo sbarco di Anzio (original Italian title) or The Battle for Anzio (UK title), is a 1968 Technicolor war film in Panavision, an Italian and American co-production, about Operation Shingle, the 1944 Allied seaborne assault on the Italian port of Anzio in World War II. It was adapted from the book "Anzio" by Wynford Vaughan-Thomas, who had been the BBC war correspondent at the battle.
Document 2: Battle of Anzio: The Battle of Anzio was a battle of the Italian Campaign of World War II that took place from January 22, 1944 (beginning with the Allied amphibious landing known as Operation "Shingle") to June 5, 1944 (ending with the capture of Rome). The operation was opposed by German forces in the area of Anzio and Nettuno. The operation was initially commanded by Major General John P. Lucas, of the U.S. Army, commanding U.S. VI Corps with the intention being to outflank German forces at the Winter Line and enable an attack on Rome.
Document 3: Battle of Monte Cassino: The Battle of Monte Cassino (also known as the Battle for Rome and the Battle for Cassino) was a costly series of four assaults by the Allies against the Winter Line in Italy held by Axis forces during the Italian Campaign of World War II. The intention was a breakthrough to Rome.
Document 4: Winter Line: The Winter Line was a series of German and Italian military fortifications in Italy, constructed during World War II by Organisation Todt and commanded by Albert Kesselring. The series of 3 lines was designed to defend a western section of Italy, focused around the town of Monte Cassino, through which ran the important Highway 6 which led uninterrupted to Rome. The primary Gustav Line ran across Italy from just north of where the Garigliano River flows into the Tyrrhenian Sea in the west, through the Apennine Mountains to the mouth of the Sangro River on the Adriatic coast in the east. The two subsidiary lines, the Bernhardt Line and the Hitler Line ran much shorter distances from the Tyrrehnian sea to just North East of Cassino where they would merge into the Gustav Line. Relative to the Gustav Line, the Hitler Line stood to the North-West and the Bernhardt Line to the South-East of the primary defenses.
Document 5: Battle of the Bulge: The Battle of the Bulge (16 December 1944 – 25 January 1945) was the last major German offensive campaign on the Western Front during World War II. It was launched through the densely forested Ardennes region of Wallonia in eastern Belgium, northeast France, and Luxembourg, towards the end of World War II. The surprise attack caught the Allied forces completely off guard. American forces bore the brunt of the attack and incurred their highest casualties of any operation during the war. The battle also severely depleted Germany's armored forces, and they were largely unable to replace them. German personnel and, later, Luftwaffe aircraft (in the concluding stages of the engagement) also sustained heavy losses.
Document 6: Battle of the Argenta Gap: The Battle of the Argenta Gap was an engagement which formed part of the Allied spring 1945 offensive during the Italian Campaign in the final stages of the Second World War. It took place in northern Italy from 12–19 April 1945 between troops of British V Corps commanded by Lieutenant-General Charles Keightley and German units of LXXVI Panzer Corps commanded by Lieutenant General ("General der Panzertruppe") Gerhard von Schwerin.
Document 7: Meuse-Argonne Offensive: The Meuse-Argonne Offensive, also known as the Maas-Argonne Offensive and the Battle of the Argonne Forest, was a major part of the final Allied offensive of World War I that stretched along the entire Western Front. It was fought from 26 September 1918 until the Armistice of 11 November 1918, a total of 47 days. The Meuse-Argonne Offensive was the largest in United States military history, involving 1.2 million American soldiers. It was one of a series of Allied attacks known as the Hundred Days Offensive, which brought the war to an end. The battle cost 28,000 German lives and 26,277 American lives. It was the largest and bloodiest operation of World War I for the American Expeditionary Force (AEF), which was commanded by General John J. Pershing, and one of the deadliest battles in American history. American losses were exacerbated by the inexperience of many of the troops, and tactics used during the early phases of the operation.
Document 8: Battle of Hürtgen Forest: The Battle of Hürtgen Forest (German: "Schlacht im Hürtgenwald" ) was a series of fierce battles fought from 19 September to 16 December 1944 between American and German forces on the Western Front during World War II in the Hürtgen Forest about 50 mi2 east of the Belgian–German border. It was the longest battle on German ground during World War II, and is the longest single battle the U.S. Army has ever fought.
Document 9: Battle of Arracourt: The Battle of Arracourt was a major clash between U.S. and German armored forces near the town of Arracourt, Lorraine, France, between 18–29 September 1944, during World War II. As part of a counteroffensive against recent U.S. advances in France, the German 5th Panzer Army had as its objective the recapture of Lunéville and the elimination of the U.S. XII Corps bridgehead over the Moselle River at Dieulouard. With local superiority in troops and tanks, the Germans anticipated quick defeat of the defending Combat Command A (CCA) of the U.S. 4th Armored Division. However, due in part to poor German tactics and the terrain, the 4th Armored Division's CCA, in concert with U.S. tactical air forces, defeated two Panzer Brigades and elements of two "Panzer" divisions in a series of engagements over an eleven-day period.
Document 10: Battle of San Pietro Infine: The Battle of San Pietro Infine (commonly referred to as the "Battle of San Pietro") was a major engagement from 8–17 December 1943, in the Italian Campaign of World War II involving Allied forces attacking from the south against heavily fortified positions of the German "Winter Line" in and around the town of San Pietro Infine, just south of Monte Cassino about halfway between Naples and Rome. The eventual Allied victory in the battle was crucial in the ultimate drive to the north to liberate Rome. The battle is also remembered as the first in which the troops of the Royal Italian Army ("Regio Esercito") fought as co-belligerents of the Allies following the armistice with Italy. The original town of San Pietro Infine was destroyed in the battle; the modern, rebuilt town of the same name is located a few hundred meters away .
Document 11: Spring 1945 offensive in Italy: The Spring 1945 offensive in Italy, codenamed Operation Grapeshot, was the final Allied attack during the Italian Campaign in the final stages of the Second World War. The attack into the Lombardy Plain by the 15th Allied Army Group started on 6 April 1945, ending on 2 May with the formal surrender of German forces in Italy.
Document 12: Operation Nordwind: Operation North Wind (German: "Unternehmen Nordwind" ) was the last major German offensive of World War II on the Western Front. It began on 31 December 1944 in Alsace and Lorraine in northeastern France, and ended on 25 January.
Document 13: Battle of Centuripe: The Battle of Centuripe was fought from 2 to 4 August 1943, as part of the Allied invasion of Sicily during World War II. The 78th "Battleaxe" Division, of the British Eighth Army, was engaged in fierce fighting around the town of Centuripe in the central portion of Sicily in the hill country between the Rivers Dittaìno and Salso. The battle focused around Centuripe which the German Wehrmacht had heavily fortified the hill town set on a very high rocky pinnacle and approached by only one steep and twisty road. Centuripe itself was the key to the whole Adrano position and the capture of Adrano would in turn force the Germans to withdraw to new positions. The British troops captured the town after heavy fighting and as a result caused the Germans to start contemplating abandoning Sicily altogether.
Document 14: 6th Panzer Army: The 6th Panzer Army ("6. Panzer-Armee") was a formation of the German Army, formed in the autumn of 1944. The 6th Panzer Army was first used as an offensive force during the Battle of the Bulge, in which it operated as the northernmost element of the German offensive. The army was subsequently transferred to Hungary in early 1945 and used in both offensive and defensive actions there. The final battles of the 6th Panzer Army were fought in Austria until the collapse of Nazi Germany, at which point the army was completely demoralized. The remnants of the army eventually surrendered to the United States Army. Army commander throughout the army's existence, SS-"Oberstgruppenführer" Josef Dietrich said in early 1945: "We call ourselves the "6th Panzer Army", because we've only got 6 Panzers left".
Document 15: Battle of Aachen: The Battle of Aachen was a major combat action of World War II, fought by American and German forces in and around Aachen, Germany, between 2–21 October 1944. The city had been incorporated into the Siegfried Line, the main defensive network on Germany's western border; the Allies had hoped to capture it quickly and advance into the industrialized Ruhr Basin. Although most of Aachen's civilian population was evacuated before the battle began, much of the city was destroyed and both sides suffered heavy losses. It was one of the largest urban battles fought by U.S. forces in World War II, and the first city on German soil to be captured by the Allies. The battle ended with a German surrender, but their tenacious defense significantly disrupted Allied plans for the advance into Germany.
ground_truth: Battle of Anzio