
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
On the complex plane, the parallelogram formed by the points 0, \( z \), \( \frac{1}{z} \), and \( z - \frac{1}{z} \) has an area of \( \frac{15}{17} \). If the real part of \( z \) is positive, let \( d \) be the smallest possible value of \( \left| z - \frac{1}{z} \right| \). Compute \( d^2 \).

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