
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
One container of paint is exactly enough to cover the inside of an old rectangle which is three times as long as it is wide.  If we make a new rectangle by shortening the old rectangle by  $18$  feet and widening it by  $8$  feet as shown below, one container of paint is also exactly enough to cover the inside of the new rectangle.  Find the length in feet of the perimeter of the new rectangle.

[asy]
size(250);
defaultpen(linewidth(0.8));
draw((-2,0)--(-2,5)--(13,5)--(13,0)--cycle^^(16,-1)--(16,6)--(27,6)--(27,-1)--cycle^^(9,5)--(9,0)^^(16,4)--(27,4));
path rect1=(13,5)--(13,0)--(9,0)--(9,5)--cycle,rect2=(16,6)--(16,4)--(27,4)--(27,6)--cycle;
fill(rect1,lightgray);
fill(rect2,lightgray);
draw(rect1^^rect2);
[/asy]

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