Let $(R,m)$ be local, $\dim R= \operatorname{depth}R=d$. Prove that every system of parameters is an $R$-sequence.

Here is my draft: $grade(I)=grade(\sqrt{I})=grade(m)=ht(m)=d \le k$ with $I=\left<a_{1},...,a_{k}\right>, (a_{i})$ is a system of parameters.

However, that is all I have. I can not prove $k\le d$. Can you help me check it?