  In anticipation of forthcoming data releases of current and future
spectroscopic surveys, we present the validation tests and analysis of
systematic effects within \texttt{velocileptors} modeling pipeline when fitting
mock data from the \texttt{AbacusSummit} N-body simulations. We compare the
constraints obtained from parameter compression methods to the direct fitting
(Full-Modeling) approaches of modeling the galaxy power spectra, and show that
the ShapeFit extension to the traditional template method is consistent with
the Full-Modeling method within the standard $\Lambda$CDM parameter space. We
show the dependence on scale cuts when fitting the different redshift bins
using the ShapeFit and Full-Modeling methods. We test the ability to jointly
fit data from multiple redshift bins as well as joint analysis of the
pre-reconstruction power spectrum with the post-reconstruction BAO correlation
function signal. We further demonstrate the behavior of the model when opening
up the parameter space beyond $\Lambda$CDM and also when combining likelihoods
with external datasets, namely the Planck CMB priors. Finally, we describe
different parametrization options for the galaxy bias, counterterm, and
stochastic parameters, and employ the halo model in order to physically
motivate suitable priors that are necessary to ensure the stability of the
perturbation theory.
