
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) = $$\frac{x^2 - x - 1}{x + 1}$$ and g(x) = -e<sup>x-1</sup> - lnx + a, for any x₁ ∈ [1, 3] and x₂ ∈ [1, 3], the inequality f(x₁) ≥ g(x₂) always holds. Determine the range of a.

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