Finite automaton for ${0^{2n} : n ge 0 } cup {(100)^m : m ge 0}$

I have to construct an FA for the following language:
$$
{ w_1,w_2 in {a,b}^* mid w_1 = 0^{2n}, w_2 = (100)^m, text{ for some } n,m in mathbb{N} }.
$$

Does anyone here have any experience with something like that? I’m totally lost how I should draw an FA for something like that. Would appreciate any kind of input or approach to this problem.