Type-I X-ray burst (XRB) light curves are sensitive to the models nuclear input and consequently affects the model-observation comparisons. $^{22}$Mg($alpha$,p)$^{25}$Al is among the most important reactions which directly impact the XRB light curve. We report the first direct measurement of $^{22}$Mg($alpha$,p)$^{25}$Al using the Active Target Time Projection Chamber. XRB light curve model-observation comparison for the source $tt{GS 1826-24}$ using new reaction rate implies a less-compact neutron star than previously inferred. Additionally, our result removes an important uncertainty in XRB model calculations that previously hindered extraction of the neutron star compactness.