Conditional Formating- Multiple Columns with Date

I am trying to format a template to highlight when dates are approaching. I am trying to get the conditional formatting to work for highlighting light red when a due date is within the next month, within the next week the cell becomes a shade darker red, and then is bright red when it is past due. I need to put a second condition in though. The attached file has a column for when a submittal is due. That is the main driver. However, I need to set it up so that when the column following it, Submittal Received, is filled in, it no longer highlights based on the due date.

Basically, I want to highlight approaching due dates with escalating shades of red as the date nears but once the item has been received, I no longer need the cells to be highlighted.

Any help would be greatly appreciated. Thank you!

Thank you so much this is wonderful. I should have fully thought through what I wanted and included this in the original post. I would love if the sheet could also highlight light red if column G is still blank 7 days after the date in column F and then be bright red if still blank 14 days after date in column F.

Again, I greatly appreciate your help!