
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
A rectangle has a perimeter of 40 units, and both its length and width are whole numbers. Find the dimensions of the rectangle that would provide the maximum possible area and confirm it is the maximum by verifying areas for slight variations in dimension.

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