The correct answer to this open question is the following.
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The most common way that prior civilization in the Americas influenced the Mayans, Inca, and Aztec was through religious beliefs and cultural aspects that were followed by the Mesoamerican civilizations.
For instance, the Toltecs, which are believed to be the ancient civilization in the Mexican region, developed a religious ceremony involving a sweat-house, among other ceremonies. The Olmecs also was one of the ancients civilizations that preceded the Mesoamerican cultures such as the Aztecs and Mayans.
Toltecs and Olmecs were polytheistic and this concept of many gods influenced the Mesoamerican and some South American civilizations.