
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
Let $f(x) = \ln x - \frac{1}{2}ax^2 - 2x$, where $a\le0$.

(Ⅰ) If the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$ is given by $y=2x+b$, find the value of $a-2b$.

(Ⅱ) Discuss the monotonicity of the function $f(x)$.

(Ⅲ) Let $g(x) = x^2 - 3x + 3$. If for any $x, t \in [0, 1]$, it always holds that $f(x) \le g(t)$, find the range of the real number $a$.

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