
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 $f(x)=x^{3}-ax^{2}+bx+c$ $(a,b,c\in\mathbb{R})$.
$(1)$ If the function $f(x)$ has extreme values at $x=-1$ and $x=3$, find the values of $a$ and $b$;
$(2)$ Under the condition of $(1)$, when $x\in[-2,6]$, $f(x) < c^{2}+4c$ always holds, find the range of values for $c$.

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