If we have a planar graph, why is it true that there always exists a vertex such that $deg(v) \leq 3$ or a face $f$ such that $deg(f) \leq 3$?

Question

If we consider $G$ to be a planar graph with no loops or multiple edges, there exists a vertex $v \in V(G)$ such that $deg(v) \leq 3$ or there exists a face that $deg(f) \leq 3$.

I'm not entirely sure why this is true, I have drawn out a few examples and can see it that way but beyond that quite unsure.