
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 area of the shaded region is 104 square inches. All angles are right angles, and all measurements are given in inches. What is the perimeter of the non-shaded region?

[asy]size(101);
filldraw(((0,0)--(0,10)--(12,10)--(12,-2)--(8,-2)--(8,0)--cycle^^(3,4)--(3,6)--(9,6)--(9,4)--cycle),gray(.6)+fillrule(1),linewidth(1));
label("$3''$",(6.5,-1),fontsize(10pt));
label("$4''$",(10,-2.7),fontsize(10pt));
label("$3''$",(4.5,5),fontsize(10pt));
label("$12''$",(6,10.7),fontsize(10pt));
label("$12''$",(13,3),fontsize(10pt));[/asy]

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