
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
Mathieu has a square plot of land. Outside this plot, there is a path of constant width with an area of \(464 \text{ m}^2\). While walking around his plot, Mathieu noticed that the difference between the lengths of the outer and inner edges of the path is \(32\) meters.

What is the total area of Mathieu's plot, including the area of the path?

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