Question: Named after John Adams, and located in New Hampshire, which mountain acts as a wall to the glacial cirque known as the The Great Gulf?

Context paragraphs:
West Branch Peabody River: The West Branch of the Peabody River is a 5.8 mi long river in the White Mountains of New Hampshire in the United States.  It is a tributary of the Peabody River, which flows into the Androscoggin River, which in turn flows south and east into Maine, joining the Kennebec River near the Atlantic Ocean.  The West Branch of the Peabody is within the Great Gulf Wilderness of the White Mountain National Forest for most of its length.  It is paralleled by the Great Gulf Trail, a popular route for backpackers.

Peel Cirque: Peel Cirque ( ) is a glacial cirque lying above the southwest portion of the Roberts Ice Piedmont, situated in the northeast portion of Alexander Island, Antarctica.  Photographed from the air by Ronne Antarctic Research Expedition (RARE) in 1947, mapped from air photographs by Falkland Islands Dependencies Survey (FIDS) in 1959, and surveyed by British Antarctic Survey (BAS), 1973–77.  Named by United Kingdom Antarctic Place-Names Committee (UK-APC) in 1980 after Dr. David Anthony Peel, glaciologist with BAS from 1968, who worked on Alexander Island, in the years 1975 and 1976.

Strawberry Cirque: Strawberry Cirque is a semi-circular glacial cirque in Antarctica, 1 nautical mile (1.9 km) wide, at the south end of Macdonald Bluffs in Miller Range.  It indents the cliff, at the north side of the terminus of Argo Glacier where the latter enters Marsh Glacier.  So named by the Ohio State University Geological Party, 1967–68, because the granite cliffs of the cirque have a bright pink to red color in certain lighting.

Huntington Ravine: Huntington Ravine is a glacial cirque on Mount Washington in the White Mountains of New Hampshire.  It is named for Joshua H. Huntington, the Principal Assistant to State Geologist Charles H. Hitchcock (1836–1919) for the Geological Survey of New Hampshire.

Riptide Cirque: Riptide Cirque ( ) is a glacial cirque on the south wall of Eastwind Ridge immediately west of Mount Naab, in the Convoy Range, Victoria Land.  Icefalls at the head provide the main ice flow into the Towle Glacier.  One of the nautical names in Convoy Range.  The name was applied by a 1989-90 New Zealand Antarctic Research Program (NZARP) field party to describe the fastest flowing tributary to Towle Glacier.

Tuckerman Ravine: Tuckerman Ravine is a glacial cirque sloping eastward on the southeast face of Mt. Washington, in the White Mountains of New Hampshire.  Although it draws hikers throughout the year, and skiers throughout the winter, it is best known for the many "spring skiers" who ascend it on foot and ski down the steep slope from early April into July.  In this period, the temperatures are relatively mild but the natural snowpack — which averages up to 55 ft in a typical winter — is still adequate to ski most seasons.  The record-setting high winds atop Mount Washington scour a massive amount of snow from the surrounding highlands and drop it here or in the adjacent Huntington Ravine.

Hockey Cirque: Hockey Cirque ( ) is a glacial cirque 0.5 nmi wide along the east wall of Ascent Glacier in the Miller Range of Antarctica.  It was so named by the Ohio State University Geological Party, 1967–68, because the cirque was the scene of a game of ice hockey.

Dike Cirque: Dike Cirque ( ) is a semi-circular glacial cirque 1 nmi wide in the Miller Range of Antarctica.  It is carved into the Macdonald Bluffs at the southeast base of Kreiling Mesa.  It was so named by the Ohio State University Geological Party, 1967–68, because the granite cliffs surrounding the cirque are cut by numerous black dikes.

Great Gulf: The Great Gulf is a glacial cirque, or amphitheater-like valley head formed from a glacier by erosion, located in the White Mountains of New Hampshire.  The cirque's walls are formed, from south to north, by the mountainsides of Mount Washington (6,288 ft/1917 m), Mount Clay (5,533 ft/1686 m), Mount Jefferson (5,716 ft/1742 m), Mount Adams (5,799 ft/1768 m), and Mount Madison (5,366 ft/1636 m).  It is drained by the West Branch of the Peabody River.

Mount Adams (New Hampshire): Mount Adams, elevation 5793 ft above sea level, is a mountain in New Hampshire, the second highest peak in the Northeast United States after its nearby neighbor, Mt. Washington.  Located in the northern Presidential Range, Mount Adams was named after John Adams, the second president of the United States.  It was given this name on July 31, 1820.  To the northeast is Mount Madison and to the southwest is Mount Jefferson.  From the summit, Mount Washington can be seen directly to the south.

Supporting paragraphs: Great Gulf Mount Adams (New Hampshire)
Answer: Mount Adams