Low rank groups of Lie type acting point and line-primitively on finite generalised quadrangles

Suppose we have a finite thick generalised quadrangle whose automorphism group G acts primitively on both the set of points and the set of lines. Then G must be almost simple. In this paper, we show that soc (G) cannot be isomorphic to Sz (2^2m+1) or Ree (3^2m+1) where m is a positive integer.