Israel-Hamas Negotiations Prisoner Releases Israel-Gaza Hostage Negotiations Qatar's Role US Involvement CIA Director Bill Burns Egypt's Role Ceasefire Agreement Humanitarian Aid Conflict Resolution High-Level Talks Cease-fire Negotiations Hostage Release Framework Proposal Negotiating Parties U.S. Involvement CIA Director William Burns Israeli Participation Prospects of Reaching an Agreement High-Stakes Hostage Negotiations Israeli-Palestinian Conflict Biden Administration Involvement Criteria for Hostage Release Security Concerns U.S.-Hamas-Israel Relations Hamas Reemergence Concerns