that the State agency shall thereafter promptly determine the eligibility of each applicant household by way of verification of income other than that determined to be excluded by section 2014(d) of this title (in part through the use of the information, if any, obtained under section 2025(e) of this title and after compliance with the requirement specified in paragraph (24)), household size (in any case such size is questionable), and such other eligibility factors as the Secretary determines to be necessary to implement sections 2014 and 2015 of this title, although the State agency may verify prior to certification, whether questionable or not, the size of any applicant household and such other eligibility factors as the State agency determines are necessary, so as to complete certification of and provide an allotment retroactive to the period of application to any eligible household not later than thirty days following its filing of an application, and that the State agency shall provide each applicant household, at the time of application, a clear written statement explaining what acts the household must perform to cooperate in obtaining verification and otherwise completing the application process;