Economics Q: How does the US current account defecit resulted in the decline in the value of the US dollar?

I don’t see how the two relate to each other. Can some1 enlighten me on this issue?

Import increase–>demand for foreign currency increase–>foreign currency appreciation–>depreciation of US $

But isn’t the low value of dollar making American goods cheaper and hence helping american exports. This will reduce the deficit if not totally wipe it… Am I correct in my understanding?

Import increase–>demand for foreign currency increase–>foreign currency appreciation–>depreciation of US $–>Xport increase–>current account surplus