PSMAcTION: A Phase II/III, Open-label, International, Multicenter, Randomized Study of AAA817 Versus Standard of Care in the Treatment of Adult Participants With PSMA Positive Metastatic Castration-resistant Prostate Cancer Who Progressed on or After [177Lu]Lu-PSMA Targeted Therapy

Inclusion Criteria: ∙ * adults ≥ 18 years of age. * ECOG performance status of 0 to 2. * histopathological and/or cytological confirmation of adenocarcinoma of the prostate. * PSMA-positive disease as assessed by PSMA PET/CT scan using an approved PSMA imaging agent as protocol instructed, * castrate level of serum/plasma testosterone (\< 50 ng/dL or \< 1.7 nmol/L). * Prior treatments with an androgen receptor pathway inhibitor (ARPI) and taxane-based chemotherapy, and progressed on or after \[177Lu\]Lu-PSMA targeted therapy. * ≥ 1 metastatic lesion that is present on screening/baseline CT, MRI, or bone scan imaging obtained ≤ 28 days prior to randomization * eGFR as requested by the sponsor Exclusion Criteria: * Any investigational agents within 28 days prior to the day of randomization. * Any 225Ac-based investigational compound used prior to the day of randomization. * Participants with a history of CNS metastases who are neurologically unstable, symptomatic, or receiving corticosteroids for the purpose of maintaining neurologic integrity. * Concurrent acute kidney injury (renal failure developed between 48 hours to 7 days) or chronic kidney disease (at least 3 months of ongoing renal injury) * Baseline xerostomia ≥ Grade 2 by CTCAE v.5 * History of uncontrolled hypertension, myocardial infarction (MI), angina pectoris, or coronary artery bypass graft (CABG) within 6 months prior to ICF signature and/or clinically active significant cardiac disease * History of lymphoproliferative disease or any known malignancy or history of malignancy of any organ system within the past 5 years (except for basal cell carcinoma or actinic keratosis that have been treated with no evidence of recurrence in the past 3 months, non-invasive malignant colon polyps that have been removed). Other protocol-defined inclusion/exclusion criteria may apply.