Finding Intersection of Circle and Line

In a two-dimensional coordinate plane, consider the circle defined by the equation:

$$ (x - 3)^2 + (y + 4)^2 = 25 $$

and the line defined by the equation:

$$ y = -2x + 1 $$

Determine the point of intersection between the circle and the line. Provide your answer as a grid-in, representing the x-coordinate, followed by the y-coordinate of the intersection point, written as an ordered pair.