
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 $f(x) = \ln x + \frac{a}{x+1}$ ($a \geq 0$),
1. When $a=3$, find the slope of the tangent line to the curve $y=f(x)$ at the point $(1, f(1))$;
2. Discuss the monotonicity of the function $f(x)$;
3. When the function $f(x)$ has an extreme value, if for all $x > 0$, $f(x) \leq (2016-a)x^3 + \frac{x^2 + a - 1}{x + 1}$ always holds, find the range of the real number $a$.

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