
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
(The full score of this question is 12 points) Given the function $f(x) = x^3 - x^2 + bx + c$.
(1) If $f(x)$ is an increasing function on $(-\infty, +\infty)$, find the range of values for $b$;
(2) If $f(x)$ takes an extreme value at $x = 1$, and $f(x) < c^2$ always holds when $x \in [-1,2]$, find the range of values for $c$.

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