"See Aztec Empire. The Aztecs used two different calendar systems, one with a cycle lasting 260 days and the other with a 365-day cycle. The 260-day calendar cycle, known as the tonalpohualli (counting of the days), was a sacred calendar used mainly by priests to predict the future.
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There were Daykeepers that kept track of the days. I hope this helped.
They should both restate the claim. Your conclusion could have a Call To Action which tells the reader that you are giving a reference to him/her.
Most transitions are going to be Two Paragraphs! I took college English and my professor wanted us to change topics/ideas every 2-3 paragraphs :)