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I've merged two image collections after calculating median values by month in each collection from 2000 to 2018. However I need to carry out an operation that needs the "sytem:time.start" field that was lost after calculating the monthly means. Therefore, I would like to know how to add a property within each image of the collection from a list representing month and year? The only property I have now in my collection is "system:index".

The code can be accessed by this link. The collection I want to associate with "system:time.start" information is on line 164, named "joined_collections"