
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 $f$ is defined on the complex numbers by $f(z)=(a+bi)z^2,$ where $a$ and $b$ are real numbers. This function has the property that for each complex number $z$, $f(z)$ is equidistant from $z^2$ and the origin. Given that $|a+bi|=10$, find $b^2.$

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