
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 say a complex number $z$ is five-presentable if there is a complex number $w$ of absolute value $5$ such that $z = w - \frac{1}{w}$. Let $T$ be the set of all five-presentable complex numbers. The set $T$ forms a closed curve in the complex plane. What is the area inside $T$?

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