A 3-year-old boy presents with developmental delay, hypotonia, and hepatomegaly. Laboratory investigations reveal elevated plasma ammonia (180 µmol/L), normal liver function tests, and normal organic acid profile. Urine orotic acid is markedly elevated. Plasma amino acid analysis shows elevated glutamine and alanine. Genetic testing confirms a deficiency in the mitochondrial enzyme carbamoyl phosphate synthetase I (CPS I). Which of the following best explains the biochemical finding of elevated orotic acid in this patient?