
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) = (k + $\frac{4}{k}$)lnx + $\frac{4-x^{2}}{x}$, where k > 0.
(1) Discuss the monotonicity of f(x) on (0, 2);
(2) If k ∈ [4, +∞), there always exist two distinct points M(x₁, y₁) and N(x₂, y₂) on the curve y = f(x) such that the tangent lines at points M and N are parallel to each other. Find the range of x₁ + x₂.

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