I'm trying to have a point in the plane which can be manipulated both using Locator as well as inserting its $x$ and $y$ coordinates. My attempts at doing this are:
Manipulate[Graphics[Point[p], PlotRange -> 1], {{p, {1, 1}}, Locator},
{p[[1]], -1, 1}, {p[[2]], -1, 1}]
which doesn't even run, as well as
Manipulate[Graphics[Point[p], PlotRange -> 1], {{p, {1, 1}}, Locator},
{p[1], -1, 1}, {p[2], -1, 1}]
which runs, but fails to see that p[1], p[2] should be the coordinates of p.
I've managed to use a 2DSlider:
Manipulate[Graphics[Point[p], PlotRange -> 1], {{p, {1, 1}}, Locator},
{p, {-1, -1}, {1, 1}}]
but even here, I can't input the exact coordinates.
My question is:
How can one give the exact coordinates of the point p in Manipulate, as well as control its position using a Locator?


