
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 $f(x)=\dfrac{1}{3}x^{3}-ax^{2}+\left(a^{2}-1\right)x+b$, and the tangent line at the point $\left(1,f(x)\right)$ is $x+y-3=0$.

(1) Find the values of $a$ and $b$, and determine the intervals where the function $f(x)$ is monotonic.

(2) If the inequality $f(x) \lt c^{2}-c$ holds for $x\in \left[-2,4\right]$, find the range of values for $c$.

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