Within thirty (30) days after an initiative or referendum petition is filed, the City Secretary shall determine whether the same is properly signed by the requisite number of qualified voters. The City Secretary shall declare void any petition paper which does not have an affidavit attached thereto as required in Section 4.03 of this Article. In examining the petition, the City Secretary shall write the letters “D.V.” (declared void) in red ink opposite the names of signatories found not qualified. After completing examination of the petition, the City Secretary shall certify the results thereof to the City Council at its next regular meeting. If the certificate of the City Secretary shall show an initiative or referendum petition to be insufficient, the City Secretary shall notify the person filing the petition, and it may be amended within ten days from the date of such notice by filing a supplementary petition upon additional papers signed and filed as provided for in the original petition. Within thirty (30) days after such amendment is filed, the City Secretary shall examine the amended petition and certify as to its sufficiency. If the amended petition is then found to be insufficient, no further proceedings shall be had with regard to it.