  The extent of nucleosynthesis in models of type I X-ray bursts and the
associated impact on the energy released in these explosive events are
sensitive to nuclear masses and reaction rates around the $^{64}$Ge waiting
point. Using the well known mass of $^{64}$Ge, the recently measured $^{65}$As
mass, and large-scale shell model calculations, we have determined new
thermonuclear rates of the $^{64}$Ge($p$,$\gamma$)$^{65}$As and
$^{65}$As($p$,$\gamma$)$^{66}$Se reactions with reliable uncertainties. The new
reaction rates differ significantly from previously published rates. Using the
new data we analyze the impact of the new rates and the remaining nuclear
physics uncertainties on the $^{64}$Ge waiting point in a number of
representative one-zone X-ray burst models. We find that in contrast to
previous work, when all relevant uncertainties are considered, a strong
$^{64}$Ge $rp$-process waiting point cannot be ruled out. The nuclear physics
uncertainties strongly affect X-ray burst model predictions of the synthesis of
$^{64}$Zn, the synthesis of nuclei beyond $A=64$, energy generation, and burst
light curve. We also identify key nuclear uncertainties that need to be
addressed to determine the role of the $^{64}$Ge waiting point in X-ray bursts.
These include the remaining uncertainty in the $^{65}$As mass, the uncertainty
of the $^{66}$Se mass, and the remaining uncertainty in the
$^{65}$As($p$,$\gamma$)$^{66}$Se reaction rate, which mainly originates from
uncertain resonance energies.
