Why can't I accelerate a block to the speed of light by simply applying a constant force?

Suppose I have a block that is initially at rest, and I apply a constant force such that, according to Newtonian mechanics, it experiences a constant acceleration of 100 m/s².

My reasoning is:

• The force remains constant.

• Therefore, the acceleration remains constant.

• As long as I keep applying the force, the velocity should keep increasing.

• Eventually, after enough time, shouldn't the block reach the speed of light?

However, I often read that it is impossible for any object with nonzero rest mass to reach the speed of light.

Where exactly does my reasoning break down?