
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 $f(x)=\frac{1}{3}x^3-ax^2+bx\ (a,b\in\mathbb{R})$, with $f'(0)=f'(2)=1$.

(1) Find the equation of the tangent line to the curve $y=f(x)$ at the point $(3,f(3))$.

(2) If the function $g(x)=f(x)-4x$, $x\in[-3,2]$, find the monotonic intervals and the minimum value of $g(x)$.

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