Триггер удаление данных из связанных таблиц

CREATE TABLE `fatelook`.`user` (
    `user_id` INT NOT NULL AUTO_INCREMENT PRIMARY KEY,
    `login` VARCHAR(50) NOT NULL ,
    `password` VARCHAR(50) NOT NULL ,
    `first_name` VARCHAR(50) NOT NULL ,
    `last_name` VARCHAR(50) NOT NULL ,
    `email` VARCHAR(50) NOT NULL ,
    `city_fk` INT(11) UNSIGNED NOT NULL DEFAULT '0',
    `address` VARCHAR(50) NOT NULL ,
    `avatar` BLOB,
    `sex` VARCHAR(32) ,
    `birth_date` DATE ,
    `reg_date` TIMESTAMP DEFAULT CURRENT_TIMESTAMP,
    `role` VARCHAR(32) DEFAULT 'member' ,
    CONSTRAINT `city_fk`
        FOREIGN KEY (`city_fk` ) REFERENCES `fatelook`.`city` (`city_id` )  
)ENGINE = InnoDB DEFAULT CHARACTER SET=utf8;

CREATE  TABLE IF NOT EXISTS `fatelook`.`message` (
  `message_id` INT NOT NULL AUTO_INCREMENT PRIMARY KEY ,
  `message` TEXT NOT NULL ,
  `sender_fk` INT NOT NULL ,
  `date` TIMESTAMP DEFAULT CURRENT_TIMESTAMP ,
  CONSTRAINT `sender_fk`
    FOREIGN KEY (`sender_fk` )
    REFERENCES `fatelook`.`user` (`user_id` )
    ON DELETE NO ACTION
    ON UPDATE NO ACTION
)ENGINE = InnoDB DEFAULT CHARACTER SET=utf8;

CREATE  TABLE IF NOT EXISTS `fatelook`.`messages_private` (
  `receiver_private_fk` INT(11) NOT NULL ,
  `message_private_fk` INT NOT NULL ,
  INDEX `receive_private_fk` (`receiver_private_fk` ASC) ,
  INDEX `message_private_fk` (`message_private_fk` ASC) ,
  CONSTRAINT `receiver_private_fk`
    FOREIGN KEY (`receiver_private_fk` )
    REFERENCES `fatelook`.`user` (`user_id` ),
  CONSTRAINT `message_private_fk`
    FOREIGN KEY (`message_private_fk` )
    REFERENCES `fatelook`.`message` (`message_id` )
    ON DELETE NO ACTION
    ON UPDATE NO ACTION
)ENGINE = InnoDB DEFAULT CHARACTER SET = UTF8;

CREATE TRIGGER DELETE_PRIVATE_MESSAGE
    ON `FATELOOK`.`MESSAGE` 
    FOR DELETE
AS
    DELETE FROM 
        `FATELOOK`.`MESSAGES_PRIVATE` JOIN `FATELOOK`.`MESSAGE`
        ON MESSAGES_PRIVATE.MESSAGE_PRIVATE_fk = MESSAGE.MESSAGE_ID
    WHERE MESSAGE_PRIVATE_fk IN
        (SELECT DELETED.MESSAGE_ID FROM DELETED);
 
END