
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 $$φ(x)= \frac {a}{x+1}$$, where $a$ is a positive constant.  
(1) If $f(x)=\ln x+φ(x)$, and $$a= \frac {9}{2}$$, find the intervals where the function $f(x)$ is increasing;  
(2) If $g(x)=|\ln x|+φ(x)$, and for any $x_1$, $x_2 \in (0, 2]$, $x_1 \neq x_2$, it holds that $$\frac {g(x_{2})-g(x_{1})}{x_{2}-x_{1}} < -1$$, find the range of values for $a$.

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