
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 one rectangle, formed by matches (assuming the length of a match is 1), is one more than the perimeter of this rectangle, while the area of the second rectangle is one less than its perimeter. What are the dimensions of these rectangles?

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