  We present the results of a joint analysis of $Chandra$ X-ray and South Pole
Telescope (SPT) SZ observations targeting the first sample of galaxy clusters
at $0.3 < z < 1.3$, selected to be the progenitors of well-studied nearby
clusters based on their expected accretion rate. We develop a new procedure in
order to tackle the analysis challenge that is estimating the intracluster
medium (ICM) properties of low-mass and high-redshift clusters with ${\sim}150$
X-ray counts. One of the dominant sources of uncertainty on the ICM density
profile estimated with a standard X-ray analysis with such shallow X-ray data
is due to the systematic uncertainty associated with the ICM temperature
obtained through the analysis of the background-dominated X-ray spectrum. We
show that we can decrease the uncertainty on the density profile by a factor
${\sim}5$ with a joint deprojection of the X-ray surface brightness profile
measured by $Chandra$ and the SZ integrated Compton parameter available in the
SPT cluster catalog. We apply this technique to the whole sample of 67 clusters
in order to track the evolution of the ICM core density during cluster growth.
We confirm that the evolution of the gas density profile is well modeled by the
combination of a fixed core and a self-similarly evolving non-cool core
profile. We show that the fraction of cool-cores in this sample is remarkably
stable with redshift although clusters have gained a factor ${\sim}4$ in total
mass over the past ${\sim}9$ Gyr. This new sample combined with our new
X-ray/SZ analysis procedure and extensive multi-wavelength data will allow us
to address fundamental shortcomings in our current understanding of cluster
formation and evolution at $z > 1$.
