Why is the sigmoid activation function prone to the "vanishing gradient" problem in deep neural networks? Select all that apply.

The maximum value of its gradient is small $($less than zero$)$

It causes the outputs to "collapse" toward zero at the later layers $($closer to the output$).$

For many inputs $($large inputs and small inputs$),$ the value of the gradient is very close to zero.

It takes a long time to "saturate".