
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
Define a function $f$ on the complex numbers by $f(z) = (a + bi)z$, where $a$ and $b$ are real numbers with $a > 0$ and $b > 0$. The function has the property that for each complex number $z$, $f(z)$ is equidistant from both $z$ and the point $1 + 0i$ in the complex plane. Given that $|a + bi| = 5$, find the value of $b^2$.

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