
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
The function $f(x) = \frac{2}{x} - a\ln(x)$, where $a\in \mathbb{R}$ is given.
(Ⅰ) When $a=-1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$;
(Ⅱ) Determine the intervals of monotonicity for the function $f(x)$;
(Ⅲ) If the function $g(x) = x^2 + f(x)$ has an extremum in the interval $(0, 1)$, find the range of values for $a$.

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