  We introduce a minimal and yet comprehensive framework with $CP$- and
classical scale-symmetries, in order to simultaneously address the hierarchy
problem, neutrino masses, dark matter, and inflation. One complex gauge singlet
scalar and three flavors of the right-handed Majorana neutrinos are added to
the standard model content, facilitating the see-saw mechanism, among others.
An adimensional theory of gravity (Agravity) is employed, allowing for the
trans-Planckian field excursions. The weak and Planck scales are induced by the
Higgs portal and the scalar non-minimal couplings, respectively, once a
Coleman-Weinberg dynamically-generated vacuum expectation value for the singlet
scalar is obtained. All scales are free from any mutual quadratic
destabilization. The $CP$-symmetry prevents a decay of the pseudoscalar
singlet, rendering it a suitable WIMPzilla dark matter candidate with the
correct observational relic abundance. Identifying the pseudo-Nambu-Goldstone
boson of the (approximate) scale symmetry with the inflaton field, the model
accommodates successful slow-roll inflation, compatible with the observational
data. We reach the conclusion that a pseudo-Nambu-Goldstone inflaton, within a
classically scale-symmetric framework, yields lighter WIMPzillas.
