
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
If the function $f(x) = ax - \frac{b}{x} + c$ (where $a, b, c \in \mathbb{R}$) passes through the point $(1, 0)$, and the equation of the tangent line at $x=2$ is $y = -x + 3$,
(Ⅰ) determine the analytic expression of $f(x)$;
(Ⅱ) find the extreme values of $f(x)$.

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