  We present proofs of two new families of sum-product identities arising from
the cylindric partitions paradigm. Most of the presented expressions, the
related sum-product identities, and the ingredients for the proofs were first
conjectured by Kanade-Russell in the spirit of Andrews-Schilling-Warnaar
identities of the $A_2$ Rogers-Ramanujan type. We follow the footsteps of
Kanade-Russell while we alter the computations heavily to accomplish our goals.
