Quadrilateral MNPQ has vertices with coordinates $M(2,5)$, $N(6, 5)$, $P(6, 7)$ and $Q(2, 7)$. When the figure is rotated clockwise $270^\circ$ around point $M$ and then reflected across the line $x = 1$, what are the coordinates of the final image of point $Q$? Express your answer as an ordered pair.
Since the problem only asks for the final image of point $Q$, we only need to look at point $Q$ with respect to point $M$.  We plot the two points below and connect them:

[asy]
dot((2,5)); dot((2,7)); label("$M (2,5)$",(2,5),E); label("$Q (2,7)$",(2,7),E); draw((2,5)--(2,7));
import graph; size(4.45cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=0,xmax=12,ymin=0,ymax=12;

pen zzzzzz=rgb(0.6,0.6,0.6);

/*grid*/ pen gs=linewidth(0.7)+zzzzzz; real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

draw((12.3,0)--(0,0)--(0,12.3),Arrows(TeXHead));
label("$x$",(12.2,0),E); label("$y$",(0,12.2),N);
[/asy] When we rotate $Q$ $270^\circ$ clockwise about $M$, we arrive at $Q'=(0,5)$:

[asy]
size(150);
dot((2,5)); dot((2,7)); label("$M (2,5)$",(2,5),E); label("$Q (2,7)$",(2,7),E); dot((0,5)); label("$Q' (0,5)$",(0,5),W); draw((2,5)--(2,7));
import graph; real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=0,xmax=12,ymin=0,ymax=12;

pen zzzzzz=rgb(0.6,0.6,0.6);

/*grid*/ pen gs=linewidth(0.7)+zzzzzz; real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

draw((12.3,0)--(0,0)--(0,12.3),Arrows(TeXHead));
label("$x$",(12.2,0),E); label("$y$",(0,12.2),N);

draw(Arc((2,5),2,0,-90)); draw(Arc((2,5),2,90,0)); draw(Arc((2,5),2,180,270));
[/asy]

Reflecting $Q'=(0,5)$ about the line $x=1$ yields $Q''=\boxed{(2,5)}$.  Notice that entirely by coincidence, this is the same as point $M$.