
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
Let's define a complex number $z$ as five-presentable if there exists a complex number $w$ of absolute value $5$ such that $z = w^2 - \frac{1}{w^2}$. Let $U$ be the set of all five-presentable complex numbers. What is the area enclosed by the set $U$ in the complex plane, assuming it forms a closed curve?

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