Suppose $z$ is a complex number such that $z^3 = 100+75i$.  Find $|z|$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose $z$ is a complex number such that $z^3 = 100+75i$.  Find $|z|$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5
Suppose $z$ is a complex number such that $z^3 = 100+75i$.  Find $|z|$.
train