(C) and oxygen (O). During the early AGB phase these stars are O-rich, showing a photospheric C/O-ratio$<$1, and most of them can be classified as stars of spectral type M. For AGB stars with initial masses up to $\approx$4$M_\odot$ the atmospheric chemical composition can change dramatically because processed elements, most notably , are dredged up to the surface by convective mixing after a thermal pulse. Depending on the C/O-ratio, their spectral type changes from K or M via S to C (C/O$\geq$1) (Groenewegen [@groene2]). For AGB stars with initial masses $\gtrsim 4M_{\odot}$ the temperature at the bottom of the convective envelope rises sufficiently high to transform C into N. This process, called hot-bottom-burning, causes some AGB star to remain O-rich.

Long-period variables (LPVs) is the generic term for variable stars known as Mira variables and semi-regular variables. They generally show periodic variations in brightness with periods of $\approx$30 up to a few thousands of days and amplitudes ranging from several tenths to approximately ten magnitudes in the visual. By studying LPVs in the Large Magellanic Cloud (LMC), Wood et al. ([@woodb]) and Wood ([@woodc]) were the first to discover that all LPVs seem to group around at least five almost 