Relation between supremum of quadratic variation expectation with expectation of supremum of martingale

Question

Let $X$ be a local martingale. Then the quadratic variation $[X]$ is such that $X^2-[X]$ is a local martingale.

I am tasked with showing that $$\sup_{t\geq0}\mathbb{E}([X]_t)<\infty\iff\mathbb{E}\left(\sup_{t\geq0}X_t^2\right)<\infty$$ and I'm not sure how to do this using the properties of local martingales. Any help would be greatly appreciated, thanks!