
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 the function $f(x)=\frac{1}{3} x^{3}-\frac{1}{2} x^{2}+bx+c$,

(1) If $f(x)$ is an increasing function on $(-∞,+∞)$, find the range of values for $b$.

(2) If $f(x)$ attains an extreme value at $x=1$, and $f(x) < c^{2}$ always holds when $x∈[-1,2]$, find the range of values for $c$.

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