
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 diagram shows a rectangle dissected into seven non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers, find the perimeter of the rectangle.
[asy]draw((0,0)--(52,0)--(52,37)--(0,37)--(0,0));draw((15,0)--(15,15)--(0,15)); draw((15,22)--(52,22));draw((27,22)--(27,37));draw((20,15)--(20,37)); draw((28,15)--(28,22)--(20,22)); draw((15,15)--(15,17)--(28,17));[/asy]

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