
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
Consider the graph of the function $y = g(x)$, which consists of five line segments, depicted below. The distance between grid lines is 1 unit.

[asy]
size(150);
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)--(3,0)--(4,5),red);
[/asy]

Calculate the sum of the $x$-coordinates of all points where $g(x) = 2$.

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