
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 \( |c+di|=5 \), find \( d^2 \).

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