  We examine the impact of the expected reach of the LHC and the XENON1T
experiments on the parameter space of the minimal classically scale invariant
extension of the standard model (SM), where all the mass scales are induced
dynamically by means of the Coleman-Weinberg mechanism. In this framework, the
SM content is enlarged by the addition of one complex gauge singlet scalar with
a scale invariant and $CP$-symmetric potential. The massive pseudoscalar
component, protected by the $CP$-symmetry, forms a viable dark matter
candidate, and three flavors of the right-handed Majorana neutrinos are
included to account for the nonzero masses of the SM neutrinos via the see-saw
mechanism. The projected constraints on the parameter space arise by applying
the ATLAS heavy Higgs discovery prospects, with an integrated luminosity of 300
and 3000~fb$^{-1}$ at $\sqrt s = 14$~TeV, to the pseudo-Nambu-Goldstone boson
of the (approximate) scale symmetry, as well as by utilizing the expected reach
of the XENON1T direct detection experiment for the discovery of the
pseudoscalar dark matter candidate. A null-signal discovery by these future
experiments implies that vast regions of the model's parameter space can be
thoroughly explored; the combined projections are expected to confine a mixing
between the SM and the singlet sector to very small values, while probing the
viability of the TeV~scale pseudoscalar's thermal relic abundance as the
dominant dark matter component in the Universe. Furthermore, the vacuum
stability and triviality requirements of the framework up to the Planck scale
are studied and the viable region of the parameter space is identified. The
results are summarized in extensive exclusion plots, incorporating additionally
the prior theoretical and experimental bounds for comparison.
