In the triangle shown, \(n\) is a positive integer, and \(\angle A > \angle B > \angle C\). How many possible values of \(n\) are there?
\[
\begin{asy}
draw((0,0)--(1,0)--(.4,.5)--cycle);
label("$A$",(.4,.5),N); label("$B$",(1,0),SE); label("$C$",(0,0),SW);
label("$2n + 12$",(.5,0),S); label("$3n - 3$",(.7,.25),NE); label("$2n + 7$",(.2,.25),NW);
\end{asy}
\] Let's think step by step and output the final answer within \boxed{}.
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