Irregularity of $\{a^x b^y c^z : x=2y \lor y>z\}$ Show that $L=\{a^x b^y c^z : x=2y \lor y&gt;z\}$ is not regular using the pumping lemma.

I know that in order to use the pumping lemma, I have to assume that $L$ is regular. Then I know that there is a $p$ such that every $w \in L$ such that $|w| \ge p$ can be represented as $xyz$ with $|y| \ne 0$ and $|xy| \le p$, so that $xy^iz \in L$ for all $i \geq 0$. But I have not been able to choose $w \in L$ that serves me to finish with the lemma, taking into account the restrictions that $L$ has.
Suppose towards a contradiction that $L$ is regular, and let $n \ge 1$ be its pumping length.
Consider the word $a^{2n}b^nc \in L$. By the pumping lemma there is some value of $k \in \{1, \dots, n\}$ such that, for every $i \ge 0$, the word $a^{2n+(i-1)k} b^nc$ also belongs to $L$.
Picking $i=0$ yields the sought contradiction since $a^{2n-k} b^n c \not\in L$. We can then conclude that $L$ is not regular.