Whenever any special assessment shall, in the opinion of the township board, be invalid by reason of irregularities or informalities in the proceedings, or if any court of competent jurisdiction shall adjudge such assessment to be illegal, the township board shall, whether the improvement has been made or not, whether any part of the assessment has been paid or not, have power to proceed from the last step at which the proceedings were legal and cause a new assessment to be made for the same purpose for which the former assessment was made. All proceedings on such reassessment and for the collection thereof shall be conducted in the same manner as provided for the original assessment, and whenever an assessment or any part thereof levied upon any premises has been so set aside, if the same has been paid and not refunded, the payment so made shall be applied upon the reassessment.