<Solid-2023-241>, hint

By vector ,let OA=a, OB=b, OC=c, OD=d. then  OG, the centroid of triangle is (a+b+c)/3

Suppose P on GD such that GP:PD=1:3, then OP=(a+b+c+d)4.

Similarly OG' is the centroid of triangle BCD, then OG'=(b+c+d)/3. Suppose P' on G'A such that

G'P':P'A=1:3, then OP'=(a+b+c+d)/4. P'=P. P is the centroid of tetrahedron ABCD.