
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 that has been dissected into nine non-overlapping squares. Given that the width and the height of the rectangle are relatively prime positive integers, find the area of the rectangle.
[asy]draw((0,0)--(77,0)--(77,52)--(0,52)--(0,0));draw((38,0)--(38,38)--(0,38)); draw((38,31)--(77,31));draw((43,31)--(43,52));draw((28,38)--(28,52)); draw((34,38)--(34,47)--(28,47)); draw((38,38)--(38,40)--(34,40)); draw((38,40)--(43,40)); draw((34,47)--(43,47));[/asy]

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