To determine Mary's next step in constructing the circumscribed circle for triangle ABC, she can consider the following possible options:
1. **Identifying the Circumcenter:**
- Mary should locate the point where the perpendicular bisectors of the sides of the triangle intersect. This point is known as the circumcenter and will be equidistant from the vertices of the triangle.
2. **Drawing Perpendicular Bisectors:**
- The next step could involve completing the construction of the perpendicular bisectors of the sides of triangle ABC if they are not already drawn. These bisectors will intersect at the circumcenter.
3. **Checking for Accuracy:**
- Mary may need to double-check the accuracy of her constructions so far by verifying that the perpendicular bisectors intersect at a common point. This ensures the correctness of the circumscribed circle's construction.
By considering these steps, Mary can progress effectively in constructing the circumscribed circle for triangle ABC.