
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 $f(x) = \frac{1}{2}x^2 - (a + \frac{1}{a})x + \ln x$, where $a > 0$.

(1) Find the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ when $a = 2$.

(2) Find the monotonic intervals of the function $f(x)$ when $a \neq 1$.

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