
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) + $\frac{a}{x+1}$ + $\frac{a}{2}$ (where a ∈ R)
1. If a = $\frac{9}{2}$, find the monotonic intervals of f(x).
2. If f(x) ≤ $\frac{a}{2}$(x+1) always holds true, find the value of a.

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