simplification/factorization of expressions

[citron]

Hello
This report may not be about a bug but about a lack of documentation.
How do I simplify/factorize the rather big symbolic expression intersectionPointPair computed below using reduce.jl ?
Neither intersectionPointPair |> factor or Algebra.optimize(intersectionPointPair) seem to be the way to do it.

using Reduce
using Grassmann
load_package(:scope)

@basis S"∞∅+++"

A = :xa*v1 + :ya*v2 + :za*v3
B = :xb*v1 + :yb*v2 + :zb*v3
C = :xc*v1 + :yc*v2 + :zc*v3
D = :xd*v1 + :yd*v2 + :zd*v3

pA = ↑(A)
pB = ↑(B)
pC = ↑(C)
pD = ↑(D)

pO = ↑(0*v1+0*v2+0*v3)
p∞ = ↑(v∞)

AB = pA ∧ pB
CD = pC ∧ pD

planeAOB = pA ∧ pB ∧ pO ∧ v∞
planeCOD = pC ∧ pD ∧ pO ∧ v∞

S = pA ∧ pB ∧ pC ∧ pD

intersectionPointPair = planeAOB ∨ planeCOD ∨ S