
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 a region formed by eight congruent squares is 512 square centimeters. What is the perimeter of the region, in centimeters?

[asy]
draw((0,0)--(-10,0)--(-10,10)--(0,10)--cycle);
draw((0,10)--(0,20)--(-40,20)--(-40,10)--cycle);
draw((-10,10)--(-10,20));
draw((-20,10)--(-20,20));
draw((-30,10)--(-30,20));
draw((-30,20)--(-30,30)--(-50,30)--(-50,20)--cycle);
draw((-40,20)--(-40,30));
draw((-10,0)--(-10,-10)--(-30,-10)--(-30,0)--cycle);
draw((-20,0)--(-20,-10));
[/asy]

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