A crane boom of length \(L = 8.0\text{ m}\) and uniform mass \(M = 240\text{ kg}\) is attached to a vertical wall by a frictionless pin joint at its base. The boom is held at an angle of \(30^\circ\) above the horizontal by a horizontal steel cable connected to the boom at a distance \(d = 6.0\text{ m}\) from the pin joint. The cable has a maximum allowable tension of \(1.20 \times 10^4\text{ N}\) before reaching its yield limit. Taking \(g = 9.8\text{ m/s}^2\), what is the maximum downward vertical force \(F\) that can be applied to the tip of the boom without exceeding the cable's tension limit?