Priority: Chaviv and Chashuv

Opinions differ in whether you should give priority in eating to what you like the most (chaviv) or what is most important (chashuv).
Examples
Situation You like mangoes. Someone serves a platter with mangoes and dates.
Question Should you first eat a mango (chaviv) or first eat a date (chashuv—due to its being one of the Five Special Fruits)?
What To Do RMH usually recommends that people begin eating whichever fruit they prefer; that is, chaviv first.

Situation You want to eat both fruit and cake. 
What To Do You may eat the fruit first if you prefer to eat it first, even though the cake is more important.
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