
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 function \(g\) is defined on the complex numbers by \(g(z) = (c+di)z,\) where \(c\) and \(d\) are real numbers. This function has the property that for each complex number \(z\), \(g(z)\) is equidistant from both \(z\) and the origin. Given that \(|c+di| = 7\), find \(d^2.\)

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