
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 sum of the areas of two squares is 145, while the difference in their areas is 105. Additionally, consider these squares to form a rectangle by placing them adjacent to one another. Calculate the sum of the perimeters of the two squares and find the area of the rectangle formed.

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