
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 $f(x) = (m+ \frac{1}{m})\ln x + \frac{1}{x} - x$, (where the constant $m > 0$).
1. When $m=2$, find the maximum value of $f(x)$;
2. Discuss the monotonicity of $f(x)$ in the interval $(0, 1)$;
3. When $m \in [3, +\infty)$, there always exist two distinct points $P(x_1, f(x_1))$ and $Q(x_2, f(x_2))$ on the curve $y=f(x)$ such that the tangents to the curve at points $P$ and $Q$ are parallel. Find the range of values for $x_1 + x_2$.

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