
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
In a rectangle dissection puzzle, a rectangle is dissected into seven non-overlapping squares. The dimensions of the rectangle are relatively prime positive integers. Determine the perimeter of the rectangle, given that the side lengths of the squares follow the relations:
- The side of the first square plus the side of the second square equals the side of the third square.
- The side of the first square plus the side of the third square equals the side of the fourth square.
- The side of the third square plus the side of the fourth square equals the side of the fifth square.
- The side of the fourth square plus the side of the fifth square equals the side of the sixth square.
- The side of the second square plus the side of the fifth square equals the side of the seventh square.

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