
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) + $\frac{a}{x+1}$, where 'a' is a constant.

1. If a = $\frac{9}{2}$, find the range of the function f(x) on the interval [1, e]. (e is the base of the natural logarithm, e ≈ 2.72)
2. If the function g(x) = f(x) + x is a monotonically decreasing function on the interval [1, 2], find the range of values for the real number 'a'.

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