
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 graphs of three functions, labelled (1) through (3), are shown below. Note that the domain of function (1) is $$\{-3, -2, -1, 0, 1, 2, 3\}$$. Find the product of the labels of the functions which are invertible. [asy]
size(8cm);
defaultpen(linewidth(.7pt)+fontsize(8pt));
import graph;

picture pic1,pic2,pic3;

draw(pic1,(-8,0)--(8,0),Arrows(4));
draw(pic1,(0,-8)--(0,8),Arrows(4));
draw(pic2,(-8,0)--(8,0),Arrows(4));
draw(pic2,(0,-8)--(0,8),Arrows(4));
draw(pic3,(-8,0)--(8,0),Arrows(4));
draw(pic3,(0,-8)--(0,8),Arrows(4));

real g(real x) {return x^3-2x;}
real h(real x) {return x-2;}
real j(real x) {return 2-x;}

real x;

draw(pic1,graph(g,-3,3),Arrows(4));
draw(pic2,graph(h,-8,8),Arrows(4));
draw(pic3,graph(j,-8,8),Arrows(4));

label(pic1,"(1)",(0,-9));
label(pic2,"(2)",(0,-9));
label(pic3,"(3)",(0,-9));

add(pic1);
add(shift(20)*pic2);
add(shift(20,-20)*pic3);
[/asy]

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