
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 $f(x)=x^3+3x^2-9x-3$:
(I) If the tangent line to $f(x)$ at the point $(x_0, f(x_0))$ is perpendicular to the line $x - 9y + 1=0$, find the equation of the tangent line $l$;
(II) Determine the extreme values of the function $f(x)$.

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