The age of this patient drives the entire decision. At 45 she is in the perimenopausal window where abnormal uterine bleeding carries a real risk of endometrial hyperplasia or cancer, and the cardinal rule in gynaecology is that such bleeding in a woman over forty demands exclusion of malignancy before anything else is done. Her ultrasound adds weight to this concern; an endometrial thickness of 8 mm is thicker than expected and is a recognised threshold for sampling the lining. The crucial point is that imaging can measure the lining but cannot tell whether the cells are benign, precancerous or cancerous, so a tissue diagnosis is mandatory. The correct move is therefore to collect endometrial tissue, by office biopsy or curettage, and send it for histopathological examination. Jumping to a hysterectomy without a diagnosis is overtreatment, prescribing hormonal pills first could disguise an underlying cancer by temporarily controlling the bleeding, and simply following her up leaves a potential malignancy undiagnosed. So the safe and definitive next step is histopathology of the endometrium. \[\boxed{\text{Endometrial histopathology}}\]