Let $f(z) =\sum_{n=0}^{\infty} a_n z^{n}$ has ROC $1$ and that only singularities on the circle $|z|=1$ are simple poles then ...

Question

This question is from Ch-13 of Complex Variables with Applications by Ponnusamy and Silvermann.

Suppose that $\sum_{n=0}^{\infty} a_n z^n $ has radius of convergence $1$ and that only singularities on the circle $|z|=1$ are simple poles. Then prove that sequence ${a_n}$ is bounded.

I am not able to understand how should I use the condition given which means that $f(z) (z- z_0) $ is analytic ( if $z_0$ is a simple pole) but I am not getting any direction and I need help?

So, please give some hints