
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 $f(x) = 2x^2 + x - k$ and $g(x) = x^3 - 3x$, if for any $x_1 \in [-1, 3]$, there always exists an $x_0 \in [-1, 3]$ such that $f(x_1) \leq g(x_0)$ holds, then the range of real number $k$ is ______.

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