Pan camera within bounds of large image

I have a camera that I pan around a large image which works fine, however when I reach the end of the image I can keep panning on and on, forver. I have looked everywhere for an answer on how to prevent this but the only one I found did not use panning and I could not get it to work.

My code atm is very simple:

map.setPosition(-map.getWidth()/2, -map.getHeight()/2);

public boolean pan(float x, float y, float deltaX, float deltaY) {
        cam.translate(-deltaX * PAN_SPEED, deltaY * PAN_SPEED);
        cam.update();
        return true;
    }

My Image is very large, 4096x4096, and my camera is 480x800. My problem is I have no idea how to get the distance I have panned, and even if I did I dont know how to stop a pan from moving past a certain point, just setting camera position won’t work because then there will be a “bounce” back.

Basically I have a rectangle inside another rectangle, and the inner rectangle should not be allowed to move outside the larger. But as I said I don’t really know where to start since I can’t get the panning distance.

Ex of something I’ve tried:

@Override
public boolean touchDown(float x, float y, int pointer, int button) {
    startX = x * PAN_SPEED;
    return false;
}

@Override
public boolean pan(float x, float y, float deltaX, float deltaY) {
    if(-totalX > map.getX() + cam.viewportWidth/2){
        cam.translate(-deltaX * PAN_SPEED, deltaY * PAN_SPEED);
        cam.update();
    }
    return true;
}

@Override
public boolean panStop(float x, float y, int pointer, int button) {
    endX = x* PAN_SPEED;
    totalX += endX - startX;
    System.out.println("pan: " + totalX + ", map: " + map.getX());
    return true;
}

This is just a test, basically I can’t move anymore after I hit the left border of the image, but totalX still keeps adding up so this will not work.

EDIT: Got it to work, code below:

@Override

public boolean pan(float x, float y, float deltaX, float deltaY) {
        cam.translate(-deltaX, deltaY);
        keepCameraInBounds();
        cam.update();
    return true;
}

private void keepCameraInBounds () {
    OrthographicCamera c = this.cam;
    Vector3 camPos = c.position;
    float HW = c.viewportWidth / 2, HH = c.viewportHeight / 2;
    camPos.x = MathUtils.clamp(camPos.x, map.getWidth()/2 - map.getWidth() + HW, map.getWidth() - map.getWidth()/2 - HW);
    camPos.y = MathUtils.clamp(camPos.y, map.getHeight()/2 - map.getWidth() + HH, map.getHeight() - map.getHeight()/2 - HH);
}