
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 $f(x) = ax + \frac{2a-1}{x} +1-3a \, (a>0)$.
(Ⅰ) When $a=1$, find the equation of the tangent line to the function $y=f(x)$ at the point $(2, f(2))$ (expressed in standard form).
(Ⅱ) If the inequality $f(x) \geq (1-a)\ln x$ always holds for $x \in [1, +\infty)$, find the range of values for the real number $a$.

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