
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 $f(x)=\ln x+ \frac{b}{x+1}$ $(b > 0)$, for any $x\_1$, $x\_2 \in [1,2]$, $x\_1 \neq x\_2$, we have $\frac{f(x\_1)-f(x\_2)}{x\_1-x\_2} < -1$. Determine the range of values for the real number $b$.

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