Out of C and CO, which is a better reducing agent for ZnO?

The free energy formation (  ΔfGo ) of CO from C becomes lower at temperatures above 1120K whereas that of CO2 from C becomes lower above 1323K than   ΔfG0 of ZnO. However,   Δ fG0 of CO2 from CO is always higher than that of ZnO. Therefore, C can reduce ZnO to Zn but not CO. therefore, out of C and CO, C is a better reducing agent than CO for ZnO.