How to pick w for the Pumping lemma if the language has no clear pattern?
I think your confusion lies in the fact that the language is not given in more "structured" form. Even if the language is not given as such, you are free to choose any string from the language which is more "structured" and allows you to disprove that language is regular.

Take $w=C^{2N}A^{3N}$ (or $A^{3N}C^{2N}$) where $N$ is the pumping length and $w$ is a string in your language, and then follow the proof in similar lines as in  How to prove that a language is not regular?.

You should prove by yourself that above string $w$ can not be pumped.