In winter, you like to keep your house interior at \(21.0^{\circ} \mathrm{C}\). Your geothermal heating system, which was advertised as being reversible, draws thermal energy from an underground reservoir at \(347 \mathrm{~K}\). In a cold winter, with the average outdoor temperature being \(0.0^{\circ} \mathrm{C}\), thermal energy escapes from the house at a rate of \(1000 \mathrm{~W} \pm 5 \%\). Distributing the thermal energy supplied by the heating system throughout the house requires \(180 \mathrm{~W}\) (provided by the heating system). Is your heating system reversible within your \(5 \%\) margin of error, or was the advertisement false? Ignore any inefficiency in converting electrical energy to mechanical energy.