Consider the chemical reaction $$a P_4O_{10} + b CaF_2 \rightarrow c PF_5 + d Ca_3(PO_4)_2,$$ where $a,$ $b,$ $c,$ and $d$ are unknown positive integers. The reaction mush be balanced; that is, the number of atoms of each element must be the same before and after the reaction. For example, because the number of oxygen atoms must remain the same, $$10a=8d.$$ While there are many possible choices for $a,$ $b,$ $c,$ and $d$ that balance the reaction, it is customary to use the smallest possible integers. Balance this reaction.
$a=$
$b=$
$c=$
$d=$