Fixed points of a smooth circle action on even-dimensional spheres

Question

Let $S^1$ act smoothly on $m$-dimensional sphere $S^m$ with $m$ even. Let $F\subset S^m$ be the fixed point set. I've learned in class that, by the Lefschetz fixed point formula, we have $\chi(F)=\chi(S^m)=2$ where $\chi$ is the Euler characteristic. But I can't see how the Lefscehtz fixed point theorem (https://en.wikipedia.org/wiki/Lefschetz_fixed-point_theorem) implies this result. Is the Lefschetz fixed point formula different to the Lefschetz fixed point theorem? Or is there another way to show this result?