根据图片内容，解释“几何定值问题”---28. (12 分) **Problem Description:** As shown in Figure 1, in rectangle ABCD, AB=3, BC=3√3. Point M is a moving point on side BC. Point P is on ray CD. The perpendicular bisector of line segment AM intersects lines AB, AM, AN, CD at points E, F, G, H respectively. ∠MAN = 60°. **(1)** Directly write out: ∠ACB = ______°, EH/AM = ______; **(2)** When BM = 1, find the value of EF + GH. **(3)** As shown in Figure 2, connect MG and extend it to intersect line CD at point P. ① Prove: MG = PG; ② As shown in Figure 3, draw a perpendicular from point P to line EH, intersecting EH at T and AH at Q. Connect DQ. Find the minimum value of line segment DQ. **Diagram Descriptions:** **Figure 1:** Type: Geometric figure illustrating a rectangle and intersecting lines. Main Elements: - Rectangle ABCD with vertices A, B, C, D. Sides AB and CD are vertical, AD and BC are horizontal. - Point M is on side BC. - Point N is on side AD. - Line segment AM is drawn. - Line segment AN is drawn. - A line intersects AB at E, AM at F, AN at G, and CD at H. This line is the perpendicular bisector of AM. F is the midpoint of AM. - Labels: A, B, C, D, M, N, E, F, G, H. **Figure 2:** Type: Geometric figure illustrating the setup for part (3)①. Main Elements: - Similar to Figure 1, with rectangle ABCD, M on BC, N on AD, AM, AN. - The perpendicular bisector of AM intersects AB at E, AM at F, AN at G, CD at H. - Line segment MG is drawn and extended to intersect line CD at point P. - Labels: A, B, C, D, M, N, E, F, G, H, P. **Figure 3:** Type: Geometric figure illustrating the setup for part (3)②. Main Elements: - Similar to Figure 2, with rectangle ABCD, M on BC, N on AD, AM, AN, E, F, G, H, P. P is the intersection of line MG and line CD. - Line segment AH is drawn. - Line segment EH is drawn. - A perpendicular is drawn from P to line EH, intersecting EH at T and AH at Q. - Line segment DQ is drawn. - Labels: A, B, C, D, M, N, E, F, G, H, P, T, Q.