Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequences

Under $\mathfrak{p}=\mathfrak{c}$, we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality $\mathfrak{c}$ , by showing that if a non-torsion Abelian group of size continuum admits a countably compact Hausdorff group topology, then it admits a countably compact Hausdorff group topology with non-trivial convergent sequences.