
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) = ax lnx, the tangent line on the graph at point (1, f(1)) is perpendicular to the line y = -1/2x.
1. Find the analytical expression of function f(x).
2. If f(x) - mx + 2 ≥ 0 for all x ≥ 1, find the range of real number m.

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