The correct statements that describe cyanobacteria are:
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They were among the first photosynthesizing organisms - Cyanobacteria are believed to be one of the earliest groups of organisms to perform photosynthesis, using sunlight to convert carbon dioxide and water into glucose and oxygen.
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They contributed to increasing levels of oxygen in the atmosphere - Cyanobacteria played a crucial role in the Great Oxygenation Event, which significantly increased the amount of oxygen in the Earth's atmosphere, making it more hospitable for aerobic life forms.
The other statements regarding cyanobacteria decreasing atmospheric oxygen levels and having complex cells containing a nucleus are incorrect, as cyanobacteria are prokaryotic organisms and do not have a nucleus.