
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 the function $f(x) = ax + \frac{1}{x} + b$ be defined on the interval $(0, +\infty)$, where $a > 0$.

(1) Find the minimum value of $f(x)$.

(2) If the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ is $y = x$, find the values of $a$ and $b$.

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