
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 $f(x)=ax+\frac{b}{x} (a,b \in \mathbb{R})$, its graph passes through point $P(1,f(1))$, and the equation of the tangent line at point $P$ is $y=3x-8$.

1. Find the values of $a$ and $b$.
2. Find the extreme values of function $f(x)$.

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