Compute \( \iint_{S} \mathbf{F} \cdot d \mathbf{S} \) for \( \mathbf{F}=\langle x y, 7 y, 0\rangle, S \) being the cone \( z^{2}=x^{2}+y^{2}, x^{2}+y^{2} \leq 25, z \geq 0 \), with the normal pointing downward.
(Give an exact answer. Use symbolic notation and fractions where needed.)
\[
\iint_{S} \mathbf{F} \cdot d \mathbf{S}=
\]
\( \square \)