If \( \cot \alpha = 1 \) and \( \sec \beta = -\tfrac{5}{3} \), where \( \pi < \alpha < \tfrac{3\pi}{2} \) and \( \tfrac{\pi}{2} < \beta < \pi \), then the value of \( \tan(\alpha + \beta) \) and the quadrant in which \( \alpha + \beta \) lies, respectively are:
