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).