
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
Given that $f(x) = \frac{1}{3}x^3 + \frac{1}{2}(b-1)x^2 + b^2x$ (where $b$ is a constant) has an extremum at $x=1$, then the value of $b$ is ______.

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