
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The complete graph of \( y = f(x) \), consisting of five line segments, is given below. The distance between grid lines is 1 unit. Determine the sum of the \( x \)-coordinates of all points where \( f(x) = x+2 \), after superimposing \( y = x+2 \) on the original graph.

[asy] 
size(200); 
real ticklen=3; 
real tickspace=2; 

real ticklength=0.1cm; 
real axisarrowsize=0.14cm; 
pen axispen=black+1.3bp; 
real vectorarrowsize=0.2cm; 
real tickdown=-0.5; 
real tickdownlength=-0.15inch; 
real tickdownbase=0.3; 
real wholetickdown=tickdown; 
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) { 

import graph; 

real i; 

if(complexplane) { 

label("$\textnormal{Re}$",(xright,0),SE); 

label("$\textnormal{Im}$",(0,ytop),NW); 

} else { 

label("$x$",(xright+0.4,-0.5)); 

label("$y$",(-0.5,ytop+0.2)); 

} 

ylimits(ybottom,ytop); 

xlimits( xleft, xright); 

real[] TicksArrx,TicksArry; 

for(i=xleft+xstep; i<xright; i+=xstep) { 

if(abs(i) >0.1) { 

TicksArrx.push(i); 

} 

} 

for(i=ybottom+ystep; i<ytop; i+=ystep) { 

if(abs(i) >0.1) { 

TicksArry.push(i); 

} 

} 

if(usegrid) { 

xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);

yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);

} 

if(useticks) { 

xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));

yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));

} else { 

xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));

yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));

} 
}; 
rr_cartesian_axes(-5,5,-5,5); 
draw((-4,-5)--(-2,-1)--(-1,-2)--(1,2)--(2,1)--(4,5),red); 
draw((-5,-3)--(5,7),blue+dotted); 
[/asy]

Present the answer in LaTex format: \boxed{Your answer}
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