Which tool allows an ArcGIS user to modify the boundary between two polygon features while ensuring they remain coincident?

The Reshape Edge tool is specifically designed to modify the boundary between two polygon features while keeping them aligned to one another. This tool allows users to click on the shared edge and adjust it, ensuring that the alterations made to one polygon will simultaneously reflect on the adjacent polygon. This functionality is crucial for maintaining topological integrity, which is essential in geographic information systems to prevent data errors such as overlapping features or gaps.

The Reshape Feature tool, while useful for altering the shape of a polygon, does not inherently ensure the coincidence of two adjacent polygons. It affects a single polygon rather than the relationship between two. The Cut Polygons tool is used to divide polygon features into multiple parts but does not focus on maintaining a coincident boundary with another polygon. The Edit Vertices tool allows for manipulation of individual vertices on a polygon but does not provide a method to keep two polygon boundaries aligned during the editing process. Therefore, the Reshape Edge tool stands out as the best option for ensuring that modifications to boundary lines happen in a coordinated manner between two related polygons.