  We consider a spin-$\frac{1}{2}$ kagome-like chain with competing ferro- and
antiferromagnetic anisotropic exchange interactions. The ground state phase
diagram of this model consists of the ferromagnetic and ferrimagnetic phases.
We study the ground state and the low-temperature properties on the phase
boundary between these phases. The ground state on this phase boundary is
macroscopically degenerate and consists of localized magnon states. We
calculate the ground state degeneracy and corresponding residual entropy. The
spontaneous magnetization has a jump on the phase boundary confirming the
first-order type of the phase transition. In the limit of a strong anisotropy
the spectrum of the low-energy excitations has multi-scale structure governing
the peculiar features of the specific heat behavior.
