Immediately upon the denial of any application for a license the board shall notify the applicant in writing. Within 10 days after the board mails the notice, the applicant may present his or her written petition for a license to the board. Upon receipt by the board of the written petition, proceedings shall be conducted in accordance with Chapter 5 (commencing with Section 11500) of Part 1 of Division 3 of Title 2 of the Government Code.