
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) = $$\frac{a}{x}$$ - x + alnx.
(1) Discuss the monotonicity of f(x);
(2) Given that f(x) has two extreme points x₁, x₂, let g(x) = f(x) + $$\frac{1}{2}x^2$$ - (a-1)x - $$\frac{a}{x}$$, if there exists an a ∈ R such that g(x₁) + g(x₂) > t(x₁ + x₂), find the range of t.

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