Conditional Format in one call for dates/blanks in another cell

Hey Brainiac's,

I hope you are all doing great for 2023 so far?

On the attached, I am looking for a conditional format to change the colour of the names in column C, based the details in column O & P.

Rules:

If the cell in column O is blank, the cell in column C to change colour to orange
If the date in column O is 10 or more days away from todays date, the cell in column C changes to red
If the cell in column P has a date, then the cell in column C turns green, this overrides the above two rules.

Any help will be much appreciated.

Thanks in advance.

Take a look at this

Maybe the green formula should be:

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