The purpose of this research is to study the safety and effects of single-dose psilocybin 25mg versus an active placebo (single dose psilocybin 1mg) in the treatment of anxiety, depression, and existential distress (i.e. loss of meaning and hope; fear of death) in advanced cancer (i.e. stage 3 or 4). Study medications will be administered in conjunction with brief psychotherapy that is designed to treat anxiety, depression and existential distress in advanced cancer. This trial is designed to evaluate efficacy and psychological mechanisms of single-dose psilocybin-assisted psychotherapy (PAP) to treat psychiatric (depression, anxiety) and existential distress (demoralization, death anxiety), and quality-of-life (QOL), in 200 outpatients with late-stage (stage 3 or 4) cancer. The study will assess the strength and durability of therapeutic effects in a double-blind, parallel-design, placebo-controlled, two-center RCT comparing a single 25mg oral 'high' dose of psilocybin to a single 1mg 'very low' (clinically non-therapeutic) dose active control psilocybin, both delivered in conjunction with a psychotherapy platform. https://clinicaltrials.gov/ct2/show/NCT05398484