Atualizar tabela mysql no comando Inserir

DELIMITER $$ 
CREATE TRIGGER after_insert  -- remove ;
AFTER INSERT ON table_first
  FOR EACH ROW BEGIN 
    INSERT INTO table_second 
      (value1, rvalue2, value3)
    VALUES 
      ('123456', '654321', 'hello trigger');    -- add ;
  END
$$ -- add $$

DELIMITER ;