Why does the temperature of a cooling liquid remains constant whilst there are both liquid and solid phases present
Thank you

All the energy supplied to the system is used for the changing of state.

Changing temperature implies increasing the kinetic energy of the particles within the liquid, solid, or gas.

Changing the state of the substance implies breaking the bonds that bind every particle.

Also, temperature depends on the kinetic energy only in this case. Whilst bonds are broken during change of state, the speed of particles is not changing.