
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 functions f(x) = xlnx and g(x) = -x^2 + ax - 3.

1. Find the minimum value of function f(x).
2. For all x ∈ (0, +∞), if 2f(x) ≥ g(x) always holds true, find the range of real number a.

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