
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 $f(x)= \frac{1}{3}x^{3}+bx^{2}+cx (b,c \in \mathbb{R})$, $f′(1)=0$, and when $x \in [-1,3]$, the minimum value of the slope of the tangent line to the curve $y=f(x)$ is $(-1)$. Find the values of $b$ and $c$.

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