Section 13. Any city or town may, by the adoption, amendment or repeal of local ordinances or by-laws, exercise any power or function which the general court has power to confer upon it, which is not inconsistent with the constitution or laws enacted by the general court in conformity with powers reserved to the general court by section 8 of Article LXXXIX of the Amendments to the Constitution and which is not denied, either expressly or by clear implication, to the city or town by its charter. Whenever appropriations, appointments, orders, regulations or other legislative or executive actions within the scope of any such ordinance or by-law are necessary in the exercise of any power or function authorized by such ordinance or by-law, any such actions which are to be taken by a city council or town meeting may be taken by ordinance, by-law, resolution, order or vote, and any such actions which are to be taken by executive officers may be taken in any appropriate manner, subject, however, as to both such categories, to all provisions of the ordinance or by-law in question, the city or town charter, and other applicable law. Any requirement that an ordinance or by-law be entitled as such, or that it contain the word ”ordained,” ”enacted” or words of similar import shall not affect the validity of any action which is required to be taken by ordinance or by-law. Nothing in this section shall be construed to permit any city or town, by ordinance or by-law, to exercise any power or function which is inconsistent with any general law enacted by the general court before November eighth, nineteen hundred and sixty-six which applies alike to all cities, or to all towns, or to all cities and towns, or to a class of not fewer than two. No exercise of a power or function denied to the city or town, expressly or by clear implication, by special laws having the force of a charter under section nine of said Article, and no change in the composition, mode of election or appointment, or terms of office of the legislative body, the mayor or city manager or the board of selectmen or town manager, may be accomplished by by-law or ordinance. Such special laws may be made inapplicable, and such changes may be accomplished, only under procedures for the adoption, revision or amendment of a charter under this chapter.