
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) = x² + $\frac{2}{x}$, g(x) = ($\frac{1}{2}$)² + m. If for all x₁ ∈ [1, 2], there exists x₂ ∈ [-1, 1] such that f(x₁) ≥ g(x₂), then the range of the real number m is _______.

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