Mathematics Question from JEE Main 2023 · 25 January, Shift 1

Let the equation of the plane passing through the line $x - 2y - z - 5 = 0 \quad \text{and} \quad x + y + 3z - 5 = 0,$ and parallel to the line $x + y + 2z - 7 = 0 \quad \text{and} \quad 2x + 3y + z - 2 = 0,$ be $ax + by + cz = 65$. Then the distance of the point $(a, b, c)$ from the plane $2x + 2y - z + 16 = 0$ is _____.