
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 $f(x)=\frac{1}{3}x^3-ax^2+(a^2-1)x+b$, where $(a,b \in \mathbb{R})$
(I) If $x=1$ is an extreme point of $f(x)$, find the value of $a$;
(II) If the equation of the tangent line to the graph of $y=f(x)$ at the point $(1, f(1))$ is $x+y-3=0$, find the maximum and minimum values of $f(x)$ on the interval $[-2, 4]$.

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