
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 curve $C: y=\frac{1}{3}x^3-x^2-4x+1$, and the line $l: x+y+2k-1=0$, find the range of real numbers $k$ for which line $l$ is always above curve $C$ when $x \in [-3, 3]$.

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