Li-rich (large filled dots) and dust-rich (open squares) K giants from sample S1 in the HR diagram. Small filled dots are non-Li-rich K giants. Green symbols denote SB, as discussed in Sect. 5. Small red dots indicate the presence of regular small-amplitude variations, whereas large crosses indicate irregular small-amplitude variations (RV jitter). STAREVOL tracks (Siess et al. 2000; Siess & Arnould 2008) are labelled according to their initial mass, and correspond to solar metallicity. Tracks evolving along the core He-burning phase are depicted in blue, whereas tracks along the AGB are displayed in red. The red clump as defined by Deepak & Reddy (2019; their Fig. 1) is represented by the dashed rectangle. The bump is well visible on the 1 M_⊙ track as the hook feature located to the lower right of the red clump region.