
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 $f(x)={x}^{3}+a{x}^{2}+bx+c$ and its curve $y=f(x)$. The tangent line at point $P(1,f(1))$ on the curve is $y=3x+1$, and $y=f(x)$ has an extreme value at $x=-2$.

(I) Find the expression for $f(x)$;

(II) Find the maximum value of $y=f(x)$ on $[-3,1]$.

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