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Using formal charges can help with this. A double bonded O with two lone pairs would have a formal charge of zero, whereas if it had a single bond with three unpaired e- the formal charge would be -1, which is unfavorable. The same thing goes for F.
You need to look at electronegativity. You can see which atoms are more electronegative based on the periodic trend. Calculating formal charge will also be helpful in determining where to put double bonds, as highly electronegative atoms are able to have a negative formal charge.
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