
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 $f(x) = \ln(-x) + ax - \frac{1}{x}$ (where $a$ is a constant), it attains an extremum at $x = -1$.
(Ⅰ) Find the value of the real number $a$;
(Ⅱ) Let $g(x) = f(-x) + 2x$, find the minimum value of $g(x)$.

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