
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}
user